Research ArticlePhantom-Like Behavior in Modified Teleparallel Gravity

Sakineh Karimzadeh 12 and Raheleh Shojaee 3

1Department of Physics Faculty of Basic Sciences University of Mazandaran PO Box 47416-95447 Babolsar Iran2Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) P O Box 55134-441 Maragha Iran3Department of Physics Azarbaijan Shahid Madani University PO Box 53714-161 Tabriz Iran

Correspondence should be addressed to Raheleh Shojaee rshojaeeazarunivacir

Received 18 October 2018 Revised 18 January 2019 Accepted 4 February 2019 Published 20 March 2019

Academic Editor Sunny Vagnozzi

Copyright copy 2019 SakinehKarimzadeh andRaheleh ShojaeeThis is an open access article distributed under theCreativeCommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The recent data from Planck2018 shows that the equation of state parameter of effective cosmic fluid today is1199080 = minus103plusmn003Thisindicates that it is possible for the universe to be in a phantom dominated era today While a phantom field is essentially capable ofexplaining this observation it suffers from some serious problems such as instabilities and violation of the null energy conditionSo it would be interesting to realize this effective phantom behavior without adopting a phantom field In this paper we studypossible realization of an effective phantom behavior in modified teleparallel gravity We show that modified teleparallel gravity isable essentially to realize an effective phantom-like behavior in the absence of a phantom field For this purpose we choose someobservationally viable 119891(119879) functions and prove that there are some subspaces of the models parameter space capable of realizinga phantom-like behavior without adopting a phantom field

1 Introduction

Different cosmological observations of the last two decadessuch as measurements of luminosity distances of Super-nova Type Ia (SNIa) [1 2] the cosmic microwave back-ground (CMB) temperature anisotropy through the Wilkin-son Microwave Anisotropy probe (WMAP) satellite [3ndash5]large scale structure [6] the integrated Sachs-Wolfe effect [7]and more recently the Planck satellite data [8 9] show thatthe universe is currently in a positively accelerating phase ofexpansion Since general relativity with ordinary matter andenergy components cannot explain such a novel observationdifferent solutions have been proposed to justify this latetime cosmic speed-up There are generally two approachesto explain this observation by modification of Einsteinrsquos fieldequations The first approach attempts to modify the energymomentum (matter) part of the field equations by adding ayet unknown component dubbed dark energy and the secondapproach tries to modify the geometric part of the fieldequations Scalar fields dark energy models [10ndash12] belongto the first category while modified gravity theories such as119891(119877) gravity [13 14] Gauss-Bonnet and 119891(119866) gravity [15 16]massive gravity [17] Lovelock gravity [18] extra-dimensional

gravity [19 20] Teleparallel Equivalent of General Relativity(TEGR) [21ndash25] and 119891(119879) gravity [26ndash28] belong to thesecond category A simple candidate for dark energy proposalis the cosmological constant [29 30] and the correspondingcosmological model (the ΛCDM) has very good agreementwith recent observational data But this scenario has not adynamical behavior and its equation of state parameter staysalways at minus1 The origin of cosmological constant is notyet well understood it needs a huge amount of fine-tuningand it is impossible to realize phantom divide line crossingin the pure ΛCDM model Because of these shortcomingswith cosmological constant in recent years attention hasbeen drawn towards modified gravity theories and amongthe various kinds of modified gravity models teleparallelgravity (TEGR) and 119891(119879) gravity have recently obtained alot of regard Teleparallel gravity is completely equivalent togeneral relativity at the level of equations and in this theorythe Lagrangian is written in terms of the torsion scalar 119879Much similar to the 119891(119877) gravity that one replaces 119877 by119891(119877) in the Einstein-Hilbert action of general relativity 119891(119879)gravity is an extension of TEGR that replaces 119879 by a genericfunction of torsion as 119891(119879) in teleparallel gravity In thismodel the Ricci scalar 119877 is zero since there is no curvature

HindawiAdvances in High Energy PhysicsVolume 2019 Article ID 4026856 8 pageshttpsdoiorg10115520194026856

2 Advances in High Energy Physics

instead the torsion field is considered in the framework ofEinsteinrsquos other (teleparallel) gravity In recent years variousaspects of teleparallel and modified teleparallel gravity arestudied in details (see [31ndash37] for some various works in thisfield)The observational viability of teleparallel and modifiedteleparallel gravity has been studied in [38 39]

With an effective phantom-like behavior one means thatthe effective energy density of the cosmic fluid is positiveand increases with time and at the same time the effectiveequation of state parameter stays less than minus1 [40] Typicallyfor realization of such a behavior phantom fields are consid-ered while the existence of phantom field causes instabilitiesand violates the null energy condition [41ndash43] Possiblerealization of phantom-like behavior in some cosmologicalmodels such as theDGPbraneworldmodel [44ndash46] and119891(119877)gravity is studied [47] Also possible existence of a phantom-like phase in teleparallel and alsomodified teleparallel gravitytheories have been studied in some references such as =[28 48ndash51] In this paper we study possible realization ofthe phantom-like behavior in modified teleparallel 119891(119879)gravity In order to achieve this goal we choose three viablemodels of 119891(119879) gravity and with appropriate selection of themodels parameters we show that phantom-like behavior canbe realized without any phantom fields in these models ofmodified teleparallel gravity This result is important becauseunlike phantom fields 119891(119879) gravity respects the null energycondition and more importantly matter is always stable inthis framework [52] The paper is organized as follows InSection 2 we briefly review field equations in 119891(119879) gravityIn Section 3 we choose three models of 119891(119879) in order tosee whether the adopted models have an effective phantombehavior or not For this purpose we plot the effective energydensity and the equation of state parameter versus the redshift119911 and compare the results with the latest observationaldata from Planck2018 Finally in Section 4 we present thesummary and conclusion

2 Field Equations for ModifiedTeleparallel Gravity

21 Field Equations of 119891(119879)Gravity In teleparallel (Einsteinrsquosother) gravity one needs to define four orthogonal vectorfields named tetrads which form a basis for spacetime man-ifold In this framework the manifold and the Minkowskimetrics are related as follows [21 52]

119892120583] = 120578119894119895119890119894120583119890119895] (1)

where the Greek indices run from 0 to 3 in coordinate basis ofthe manifold while the Latin indices run the same but in thetangent space of themanifold and 120578119894119895 = diag(+1 minus1 minus1 minus1) isthe Minkowski metric The connection in teleparallel gravitythat is the Weitzenbock connection is defined as follows

Γ120588120583] = 119890120588119894 120597]119890119894120583 (2)

which gives the spacetime a nonzero torsion but zero cur-vature in contrast to general relativity By this definition thetorsion tensor and its permutations are

119879120588120583] equiv 119890120588119894 (120597120583119890119894] minus 120597]119890119894120583) (3)

119870120583]120588 = minus12 (119879120583]120588 minus 119879]120583

120588 minus 119879120588120583]) (4)

119878120588120583] = 12 (119870120583]120588 + 120575120583120588119879120572]120572 minus 120575]120588119879120572120583120572) (5)

where 119878120588120583] is called the Superpotential In correspondencewith Ricci scalar we define a torsion scalar as

119879 = 119878120588120583]119879120588120583] (6)

So the gravitational action of teleparallel gravity can bewritten as follows

119868 = 116120587119866 int1198894119909 |119890| 119879 (7)

where |119890| equiv det(119890120572120583) = radicminus det(119892120583]) is the determinantof the vierbein 119890119886120583 which is equal to radicminus119892 Variation of thisaction with respect to the vierbeins gives the teleparallel fieldequations as follows

119890minus1120597120583 (119890119890120588119894 119878120588120583]) minus 119890120582119894 119879120588120583120582119878120588]120583 + 14119890

]119894119879 = 4120587119866119890120588119894 Θ120588] (8)

Now similar to modifying the action of general relativity inwhich 119877 is replaced by a general function 119891(119877) one canreplace the teleparallel action 119879 by a function 119891(119879) Doingthis the resulting modified field equations are

119890minus1120597120583 (119890119878119894120583]) 119891119879 (119879) minus 119890120582119894 119879120588120583120582119878120588]120583119891119879 (119879)

+ 119878119894120583]120597120583 (119879) 119891119879119879 (119879) + 14119890

]119894119891 (119879) = 4120587119866119890120588119894 Θ120588]

(9)

where Θ120588] is the energy momentum tensor of matter 119891119879 equiv119889119891119889119879 and119891119879119879 equiv 11988921198911198891198792Wenote thatwe have set the spinconnection to zero (as usually it is done in the formulationof 119891(119879) gravity) In this case the theory does not have localLorentz invariance In what follows we set 4120587119866 = 122 Cosmological Considerations Now for cosmological con-siderations we assume a spatially flat FRWmetric as [34 53]

119890120583120572 = diag (1 minus119886 (119905) minus119886 (119905) minus119886 (119905)) (10)

where 119886(119905) is the scale factor of the universe For Lagrangiandensity we obtain

119879 = minus6( 119886119886)2

= minus61198672 (11)

where 119867 = 119886119886 is the Hubble parameter Therefore thecosmological field equations become

121198672119891119879 (119879) + 119891 (119879) = 16120587119866120588 (12)

and

481198672119891119879119879 (119879) minus 4 ( + 31198672)119891119879 (119879) minus 119891 (119879)= 16120587119866120588

(13)

Advances in High Energy Physics 3

where 120588 and 119901 are the ordinary matter energy density andpressure respectively The conservation equation in thisframework is as follows

120588 + 3119867 (120588 + 119901) = 0 (14)

Now (12) and (13) can be rewritten as follows

1198672 = 161205871198663 (120588 + 120588(119879)) (15)

and

2 + 31198672 = minus8120587119866(119875 + 119875(119879)) (16)

where119875(119879) and 120588(119879) are the energy density and pressure of thetorsion fluid that are defined as follows respectively

120588(119879) = 2119879119891119879 (119879) minus 119891 (119879) minus 11987916120587119866 (17)

119875(119879) = 4 (2119879119891119879119879 (119879) + 119891119879 (119879) minus 1) minus 120588(119879)16120587119866 (18)

Finally the equation of state parameter of the torsion fluid120596(119879) is defined as

120596(119879) equiv 119875(119879)120588(119879) = minus1 + 4 (2119879119891119879119879 (119879) + 119891119879 (119879) minus 1)

2119879119891119879 (119879) minus 119891 (119879) minus 119879 (19)

Note that if we consider 119891(119879) = 119879 + 119865(119879) then (17) and (19)can be rewritten as follows

120588(119879) = 2119879119865119879 minus 11986516120587119866 (20)

120596(119879) = minus1 + (119865 minus 2119879119865119879 minus 119879) (119865119879 + 2119879119865119879119879)(1 + 119865119879 + 2119879119865119879119879) (119865 minus 2119879119865119879) (21)

respectively With these preliminaries in the next section westudy possible realization of the phantom-like behavior insome observationally viable 119891(119879)models

3 Phantom-Like Behavior in 119891(119879) GravityTo have an effective phantom-like behavior the effectiveenergy density must be positive and growing positively withtime Also the equation of state parameter should be lessthan minus1 It has been shown that modifying the geometricpart of the Einstein field equations alone leads to an effectivephantom-like behavior while there is no phantom field in theproblem (see [44ndash47]) Now we show that modified telepar-allel gravity (119891(119879) gravity) can realize an effective phantom-like behavior while the null energy condition for the effectivecosmic (torsion) fluid that is (120588(119879) + 119875(119879) ge 0) is respectedWe note that as has been shown in [52]matter is always stablein these theories To see the phantom-like behavior of 119891(119879)gravity we adopt some models of 119891(119879) gravity that could beviable through for instance cosmological and solar systemtests In this respect we consider a scale factor of the type

119886 (119905) = (1199052 + 11990501 minus ]

)1(1minus]) (22)

This scale factor has two adjustable parameters 1199050 and ] andby assumption ] = 1 This choice is coming from bouncingcosmological solutions in the context of string theory withquintom matter [54] Note that this choice belongs to theclass of scale factors 119886(119905) = 1198860119905119899 that are usually adopted inliterature Based on the definition 1 + 119911 = 1119886(119905) with thischoice of the scale factor and (11) we find

119879 = minus24 (1 (1 + 119911)1minus] minus 1199050 (1 minus ])) (1 + 119911)2(1minus])(1 minus ])2 (23)

We note that it is easy to show that the scale factor (22)with two adjustable parameters 1199050 and ] is essentially asolution of the field equations So in what follows we explorepossible realization of the effective phantom-like behaviorwith adopted 119891(119879) functions31 Phantom-Like Effect with 119891(119879) = 119879 + 1198910(minus119879)119901 Inthis form of 119891(119879) 1198910 and 119901 are two modelrsquos dimensionlessparameters in which only 119901 is an independent parameter Aswe can see for 119901 = 0 this type of 119891(119879) gravity can reduce toΛ119862119863119872 cosmology while for 119901 = 12 it reduces to the DvaliGabadadze and Porrati (DGP) braneworld model Inserting119891(119879) = 119879 + 1198910(minus119879)119901 into the first Friedmann equation (12)and calculating the result for the present time we obtain 1198910as follows [34]

1198910 = 1 minus Ω1198980(611986720)119901minus1 (2119901 minus 1)

(24)

where Ω1198980 and 1198670 are the dimensionless density parameterof the dust matter and the present Hubble parameter respec-tively We note that in order to have a positively acceleratingexpansion of the universe we need those values of 119901 where119901 lt 1 [55] Now for this type of 119891(119879) gravity we find that(remember that 119891(119879) equiv 119879 + 119865(119879))

119865 (119879) = 1198910 (minus119879)119901 (25)

119865119879 = minus1198910119901 (minus119879)119901minus1 (26)

and

119865119879119879 = 1198910119901 (119901 minus 1) (minus119879)119901minus2 (27)

By applying (20) and (21) we obtain the effective density andequation of state parameter for this model as

120588(119879) = 1198910 (minus119879)119901 (2119901 minus 1)16120587119866 (28)

120596(119879) = minus1 + (1199011198910 (minus119879)119901 (1 minus 2119901) minus 119901119879)(1199011198910 (minus119879)119901 (1 minus 2119901) minus 119879) (29)

Now to see whether this model has an effective phantom-like behavior or not we plot the evolution of the effectiveenergy density and the equation of state parameter versus theredshift 119911 In this manner we obtain a suitable amount forthe independent parameter 119901 to have an effective phantom-like behavior that this amount is about 119901 = 0028 In this

4 Advances in High Energy Physics

respect by using the equations (28) and (29) Figures 1 and2 are plotted Also we have used Ω1198980 = 0315 1198670 =674119896119898119904minus1119872119901119888minus1 and ] = 195 in all numerical calculationsin the paper This value 119901 is in agreement with the resultsreported in literature In Figure 2 as we can see the effectiveequation of state parameter for the present time (119911 = 0)is 1205960 = minus103 this amount is in favor of the recent datafrom Planck2018 However we should pay attention that inthis form of 119891(119879) the effective equation of state parametercrosses the cosmological constant (phantom divide) line120596 = minus1 from phantom-like phase to the quintessence-like phase in future This behavior is not in favor of theobservational data that show transition from the quintessencephase to the phantom phase Nevertheless having a positivelygrowing energy density is a favorable capability of thismodel

32 Phantom-Like Effect with 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) Inthis model 120572 is an independent parameter and 1198790 = 119879(119911 = 0)is the current value of the torsion scalar In the limit 120572 997888rarr 0this model recovers the Λ119862119863119872 model [34] Also by usingthe modified Friedmann equation we find

120585 = minus 1 minus Ω11989801 minus (1 minus 2120572) 119890120572 (30)

In this model if 120572 gt 0 the universe has a phantom phase(with 120596 lt minus1) and if 120572 lt 0 it has a quintessence phase(with 120596 gt minus1) [48] For this form of 119891(119879) function weobtain

119865 (119879) = 120585119879 (1 minus 1198901205721198790119879) (31)

119865119879 = 1205851205721198790119879 1198901205721198790119879 + 120585 (1 minus 1198901205721198790119879) (32)

and

119865119879119879 = minus120572211987920 1205851198793 1198901205721198790119879 (33)

Once again using (20) and (21) we acquire 120588(119879) and 120596(119879) inthe present model as follows

120588(119879) = 212057212058511987901198901205721198790119879 + 119879120585 (1 minus 1198901205721198790119879)16120587119866 (34)

and

120596(119879) = minus1 + (119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879 minus 119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792))(119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792) + 1)

(35)

respectively We try to see possible realization of the effectivephantom-like behavior in this model by numerical treatmentof these quantities We investigated the behavior of 120588(119879) and120596(119879) versus the redshift 119911 for different choices of the modelparameter 120572 Our analysis shows that the phase of expansionof the universe (according to the values of 120596) depends onthe sign of the parameter 120572 We find that 120572 = 007 is theacceptable value for realization of an effective phantom-likebehavior in this model By using (34) and (35) the evolutionsof 120588(119879) and 120596(119879) versus the redshift are shown respectivelyin Figures 3 and 4 Figure 3 shows an increasing (positivelygrowing) energy density with the cosmic time (inverse of theredshift) In Figure 4 as we can see with the proper selectionof parameters this model can display 120596(119879) = minus103 forpresent time Also Figure 4 shows that the effective equationof state stays always less than minus1 in this model Therefore wenote that in this model the crossing of the phantom dividecould not occur and the universe evermore is in the phantomphase Similar to the previous case this behavior is not infavor of the observational data that shows transition from thequintessence phase to the phantom phase Therefore we canconclude that the present model is not observationally viable

33 Phantom-Like Effect with 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) +(minus119879)120573) The above two models have been used in the liter-atures for a variety of purposes Possible transition to the

phantom phase of the cosmic expansion has been treatedwith the mentioned 119891(119879)models in a context a little differentfrom our approach Here and for the sake of more novelty ofthe treatment we consider a combined model that containsa relatively more general 119891(119879) function This approach isintroduced in [48] The number of free parameters here ismore than the previous cases Usually with a wider parameterspace one expects to encounter more fine-tuning of theparameter to have cosmologically viable solutions But in thesame time it is easier in principle to find some subspaces ofthe model parameter space to fulfill the required expectationFor the sake of simplicity we have taken 120585 = 1198910 equiv 119899 and119901 = 120572 equiv 120573 Here 120573 and 119899 are two parameters of model only120573 is free parameter because 119899 can be obtained as

119899 = minus Ω1198980 minus 1(1 minus 2120573) (61198670)2120573minus2 + (1 minus (1 minus 2120573) 119890120573)

(36)

Also for this combined model we can acquire

119865 (119879) = 119899 (119879 minus 119879119890(1205731198790119879) + (minus119879)120573) (37)

119865119879 = 1198991205731198790119879 1198901205731198790119879 + 119899 (1 minus 1198901205731198790119879) minus 119899120573 (minus119879)120573minus1 (38)

and

119865119879119879 = minus1198991205732119879201198793 1198901205731198790119879 + 119899120573 (120573 minus 1) (minus119879)119901minus2 (39)

Advances in High Energy Physics 5

0 1 32z

068

(T)

070

072

074

076

078

080

Figure 1 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 1198910(minus119879)119901

W(T)

minus1minus2 1 2 30z

minus15

minus14

minus13

minus12

minus11

minus1

Figure 2 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 1198910(minus119879)119901 where the dash lines represent120596(119879)0 = minus103

Similar to the former two models by using (20) and (21) weobtain the effective density and equation of state parameterfor this model respectively as follows

120588(119879) = 119899 ((minus119879)120573 (2120573 minus 1) + 119879 + 1198901205731198790119879 (21205731198790 minus 119879))16120587119866 (40)

and

120596(119879) = minus1 + ΘΥ (41)

420

430

440

450

460

470

480

0 1 2 3minus1z

(T)

Figure 3 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)

1 2 30z

minus120minus119minus118minus117minus116minus115minus114minus113minus112minus111minus110minus109minus108minus107minus106minus105minus104minus103minus102minus101minus100minus099

W(T)

Figure 4 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) where the dash linesrepresent 120596(119879)0 = minus103

where we have defined

Θ

equiv 119899 (minus119879)120573 (1 minus 2120573) + 1198901205731198790119879 (119879119899 minus 21198991205731198790) minus 119879 (1 + 119899)(minus119879)119899 (1 minus 2120573) + 1198901205731198790119879 (119879 minus 21205731198790) minus 119879

(42)

and

Υ equiv 1 + (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + (1 minus 2120573) 120573 (minus119879)120573minus11 + 119899 (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + 119899 + 119899120573 (1 minus 2120573) (minus119879)120573minus1

(43)

6 Advances in High Energy Physics

(T)

250

300

350

400

minus1 1 2 30z

Figure 5 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573)

W(T)

minus1100minus1050

minus1minus0950minus0900minus0850minus0800minus0750minus0700minus0650minus0600minus0550minus0500

minus05 0 05 1 15 2 25 3minus1z

Figure 6 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573) where the dashlines represent 120596(119879)0 = minus103

Finally to investigate the possible realization of thephantom-like behavior in this combinedmodel by using (40)and (41) we plot 120588(119879) and 120596(119879) versus the redshift for differentvalues of 120573 We observe that the two conditions for effectivephantom mimicry (a) where the effective energy densitymust be positive and growing with time (b) the equationof state parameter should be less than minus1 are satisfied if120573 = 02 This typical behavior of 120588(119879) and 120596(119879) versus theredshift is shown in Figures 5 and 6 respectively We notethat unlike the previous two cases this model is strictly infavor of the observational data As is seen from Figure 6it is obvious that the effective equation of state parametercan cross the 120596(119879) = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1 andamount 120596(119879) for current time (119911 = 0) is consistent with theresent observational data It means that universe evolves from

quintessence-like phase towards the phantom-like phaseWe can conclude that this model is capable of realizing asuitable dynamical mechanism for getting the present timecosmic acceleration and transition to a phantom-like stagein a fascinating manner Consequently this model is morecosmologically viable than the previous two models

4 Conclusion

In this paper we have investigated possible realization ofan effective phantom behavior in some viable 119891(119879) gravitymodels With effective phantom-like behavior we mean aneffective energy density that should be positive and growingpositively with time and also the equation of state parametershould be less thanminus1We have chosen three differentmodelsof 119891(119879) gravity where two of them are reliable based onprevious studies and our third model is a combined modelWe have shown that model with 119891(119879) = 119879 + 1198910(minus119879)119901realizes an effective phantom-like behavior if 119901 = 0028As is shown in Figure 2 we obtained the effective equationof state parameter for present time about 120596(119879)0 = minus103where this amount is acceptable according to the recentdata from Planck2018 But this model evolves from effectivephantom-like phase towards the effective quintessence-likephase in future Thus this model is not in complete favorof observation since observation shows transition fromquintessence-like to phantom-like phase We have presentedanother 119891(119879) model which is 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)This 119891(119879)model realizes an effective phantom-like behaviorif 120572 = 007 Although 120596(119879)0 is obtained as an acceptable valuethat is shown in Figure 4 this 119891(119879) function is not also infavor of observation since in this model the crossing of thephantom divide could not occur and the universe evermoreis in the phantom phase Finally we have constructed a119891(119879) theory by combining the two previous models whereit only contains one model parameter 120573 This model realizesan effective phantom-like behavior if 120573 = 02 Unlike theprevious two models this model is cosmologically moreviable since the equation of state parameter in this modelevolves from effective quintessence-like phase towards aneffective phantom-like phase As is shown in Figure 6 it isobvious that 120596(119879) can cross the 120596 = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1and amount 120596(119879)0 is consistent with the resent observationaldata Therefore this combined model is in agreement withthe observational data

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

It is a pleasure to thank Professor Kourosh Nozari forhelpful discussions and valuable comments Also this work

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

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Advances in High Energy Physics 3

where 120588 and 119901 are the ordinary matter energy density andpressure respectively The conservation equation in thisframework is as follows

120588 + 3119867 (120588 + 119901) = 0 (14)

Now (12) and (13) can be rewritten as follows

1198672 = 161205871198663 (120588 + 120588(119879)) (15)

and

2 + 31198672 = minus8120587119866(119875 + 119875(119879)) (16)

where119875(119879) and 120588(119879) are the energy density and pressure of thetorsion fluid that are defined as follows respectively

120588(119879) = 2119879119891119879 (119879) minus 119891 (119879) minus 11987916120587119866 (17)

119875(119879) = 4 (2119879119891119879119879 (119879) + 119891119879 (119879) minus 1) minus 120588(119879)16120587119866 (18)

Finally the equation of state parameter of the torsion fluid120596(119879) is defined as

120596(119879) equiv 119875(119879)120588(119879) = minus1 + 4 (2119879119891119879119879 (119879) + 119891119879 (119879) minus 1)

2119879119891119879 (119879) minus 119891 (119879) minus 119879 (19)

Note that if we consider 119891(119879) = 119879 + 119865(119879) then (17) and (19)can be rewritten as follows

120588(119879) = 2119879119865119879 minus 11986516120587119866 (20)

120596(119879) = minus1 + (119865 minus 2119879119865119879 minus 119879) (119865119879 + 2119879119865119879119879)(1 + 119865119879 + 2119879119865119879119879) (119865 minus 2119879119865119879) (21)

respectively With these preliminaries in the next section westudy possible realization of the phantom-like behavior insome observationally viable 119891(119879)models

3 Phantom-Like Behavior in 119891(119879) GravityTo have an effective phantom-like behavior the effectiveenergy density must be positive and growing positively withtime Also the equation of state parameter should be lessthan minus1 It has been shown that modifying the geometricpart of the Einstein field equations alone leads to an effectivephantom-like behavior while there is no phantom field in theproblem (see [44ndash47]) Now we show that modified telepar-allel gravity (119891(119879) gravity) can realize an effective phantom-like behavior while the null energy condition for the effectivecosmic (torsion) fluid that is (120588(119879) + 119875(119879) ge 0) is respectedWe note that as has been shown in [52]matter is always stablein these theories To see the phantom-like behavior of 119891(119879)gravity we adopt some models of 119891(119879) gravity that could beviable through for instance cosmological and solar systemtests In this respect we consider a scale factor of the type

119886 (119905) = (1199052 + 11990501 minus ]

)1(1minus]) (22)

This scale factor has two adjustable parameters 1199050 and ] andby assumption ] = 1 This choice is coming from bouncingcosmological solutions in the context of string theory withquintom matter [54] Note that this choice belongs to theclass of scale factors 119886(119905) = 1198860119905119899 that are usually adopted inliterature Based on the definition 1 + 119911 = 1119886(119905) with thischoice of the scale factor and (11) we find

119879 = minus24 (1 (1 + 119911)1minus] minus 1199050 (1 minus ])) (1 + 119911)2(1minus])(1 minus ])2 (23)

We note that it is easy to show that the scale factor (22)with two adjustable parameters 1199050 and ] is essentially asolution of the field equations So in what follows we explorepossible realization of the effective phantom-like behaviorwith adopted 119891(119879) functions31 Phantom-Like Effect with 119891(119879) = 119879 + 1198910(minus119879)119901 Inthis form of 119891(119879) 1198910 and 119901 are two modelrsquos dimensionlessparameters in which only 119901 is an independent parameter Aswe can see for 119901 = 0 this type of 119891(119879) gravity can reduce toΛ119862119863119872 cosmology while for 119901 = 12 it reduces to the DvaliGabadadze and Porrati (DGP) braneworld model Inserting119891(119879) = 119879 + 1198910(minus119879)119901 into the first Friedmann equation (12)and calculating the result for the present time we obtain 1198910as follows [34]

1198910 = 1 minus Ω1198980(611986720)119901minus1 (2119901 minus 1)

(24)

where Ω1198980 and 1198670 are the dimensionless density parameterof the dust matter and the present Hubble parameter respec-tively We note that in order to have a positively acceleratingexpansion of the universe we need those values of 119901 where119901 lt 1 [55] Now for this type of 119891(119879) gravity we find that(remember that 119891(119879) equiv 119879 + 119865(119879))

119865 (119879) = 1198910 (minus119879)119901 (25)

119865119879 = minus1198910119901 (minus119879)119901minus1 (26)

and

119865119879119879 = 1198910119901 (119901 minus 1) (minus119879)119901minus2 (27)

By applying (20) and (21) we obtain the effective density andequation of state parameter for this model as

120588(119879) = 1198910 (minus119879)119901 (2119901 minus 1)16120587119866 (28)

120596(119879) = minus1 + (1199011198910 (minus119879)119901 (1 minus 2119901) minus 119901119879)(1199011198910 (minus119879)119901 (1 minus 2119901) minus 119879) (29)

Now to see whether this model has an effective phantom-like behavior or not we plot the evolution of the effectiveenergy density and the equation of state parameter versus theredshift 119911 In this manner we obtain a suitable amount forthe independent parameter 119901 to have an effective phantom-like behavior that this amount is about 119901 = 0028 In this

4 Advances in High Energy Physics

respect by using the equations (28) and (29) Figures 1 and2 are plotted Also we have used Ω1198980 = 0315 1198670 =674119896119898119904minus1119872119901119888minus1 and ] = 195 in all numerical calculationsin the paper This value 119901 is in agreement with the resultsreported in literature In Figure 2 as we can see the effectiveequation of state parameter for the present time (119911 = 0)is 1205960 = minus103 this amount is in favor of the recent datafrom Planck2018 However we should pay attention that inthis form of 119891(119879) the effective equation of state parametercrosses the cosmological constant (phantom divide) line120596 = minus1 from phantom-like phase to the quintessence-like phase in future This behavior is not in favor of theobservational data that show transition from the quintessencephase to the phantom phase Nevertheless having a positivelygrowing energy density is a favorable capability of thismodel

32 Phantom-Like Effect with 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) Inthis model 120572 is an independent parameter and 1198790 = 119879(119911 = 0)is the current value of the torsion scalar In the limit 120572 997888rarr 0this model recovers the Λ119862119863119872 model [34] Also by usingthe modified Friedmann equation we find

120585 = minus 1 minus Ω11989801 minus (1 minus 2120572) 119890120572 (30)

In this model if 120572 gt 0 the universe has a phantom phase(with 120596 lt minus1) and if 120572 lt 0 it has a quintessence phase(with 120596 gt minus1) [48] For this form of 119891(119879) function weobtain

119865 (119879) = 120585119879 (1 minus 1198901205721198790119879) (31)

119865119879 = 1205851205721198790119879 1198901205721198790119879 + 120585 (1 minus 1198901205721198790119879) (32)

and

119865119879119879 = minus120572211987920 1205851198793 1198901205721198790119879 (33)

Once again using (20) and (21) we acquire 120588(119879) and 120596(119879) inthe present model as follows

120588(119879) = 212057212058511987901198901205721198790119879 + 119879120585 (1 minus 1198901205721198790119879)16120587119866 (34)

and

120596(119879) = minus1 + (119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879 minus 119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792))(119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792) + 1)

(35)

respectively We try to see possible realization of the effectivephantom-like behavior in this model by numerical treatmentof these quantities We investigated the behavior of 120588(119879) and120596(119879) versus the redshift 119911 for different choices of the modelparameter 120572 Our analysis shows that the phase of expansionof the universe (according to the values of 120596) depends onthe sign of the parameter 120572 We find that 120572 = 007 is theacceptable value for realization of an effective phantom-likebehavior in this model By using (34) and (35) the evolutionsof 120588(119879) and 120596(119879) versus the redshift are shown respectivelyin Figures 3 and 4 Figure 3 shows an increasing (positivelygrowing) energy density with the cosmic time (inverse of theredshift) In Figure 4 as we can see with the proper selectionof parameters this model can display 120596(119879) = minus103 forpresent time Also Figure 4 shows that the effective equationof state stays always less than minus1 in this model Therefore wenote that in this model the crossing of the phantom dividecould not occur and the universe evermore is in the phantomphase Similar to the previous case this behavior is not infavor of the observational data that shows transition from thequintessence phase to the phantom phase Therefore we canconclude that the present model is not observationally viable

33 Phantom-Like Effect with 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) +(minus119879)120573) The above two models have been used in the liter-atures for a variety of purposes Possible transition to the

phantom phase of the cosmic expansion has been treatedwith the mentioned 119891(119879)models in a context a little differentfrom our approach Here and for the sake of more novelty ofthe treatment we consider a combined model that containsa relatively more general 119891(119879) function This approach isintroduced in [48] The number of free parameters here ismore than the previous cases Usually with a wider parameterspace one expects to encounter more fine-tuning of theparameter to have cosmologically viable solutions But in thesame time it is easier in principle to find some subspaces ofthe model parameter space to fulfill the required expectationFor the sake of simplicity we have taken 120585 = 1198910 equiv 119899 and119901 = 120572 equiv 120573 Here 120573 and 119899 are two parameters of model only120573 is free parameter because 119899 can be obtained as

119899 = minus Ω1198980 minus 1(1 minus 2120573) (61198670)2120573minus2 + (1 minus (1 minus 2120573) 119890120573)

(36)

Also for this combined model we can acquire

119865 (119879) = 119899 (119879 minus 119879119890(1205731198790119879) + (minus119879)120573) (37)

119865119879 = 1198991205731198790119879 1198901205731198790119879 + 119899 (1 minus 1198901205731198790119879) minus 119899120573 (minus119879)120573minus1 (38)

and

119865119879119879 = minus1198991205732119879201198793 1198901205731198790119879 + 119899120573 (120573 minus 1) (minus119879)119901minus2 (39)

Advances in High Energy Physics 5

0 1 32z

068

(T)

070

072

074

076

078

080

Figure 1 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 1198910(minus119879)119901

W(T)

minus1minus2 1 2 30z

minus15

minus14

minus13

minus12

minus11

minus1

Figure 2 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 1198910(minus119879)119901 where the dash lines represent120596(119879)0 = minus103

Similar to the former two models by using (20) and (21) weobtain the effective density and equation of state parameterfor this model respectively as follows

120588(119879) = 119899 ((minus119879)120573 (2120573 minus 1) + 119879 + 1198901205731198790119879 (21205731198790 minus 119879))16120587119866 (40)

and

120596(119879) = minus1 + ΘΥ (41)

420

430

440

450

460

470

480

0 1 2 3minus1z

(T)

Figure 3 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)

1 2 30z

minus120minus119minus118minus117minus116minus115minus114minus113minus112minus111minus110minus109minus108minus107minus106minus105minus104minus103minus102minus101minus100minus099

W(T)

Figure 4 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) where the dash linesrepresent 120596(119879)0 = minus103

where we have defined

Θ

equiv 119899 (minus119879)120573 (1 minus 2120573) + 1198901205731198790119879 (119879119899 minus 21198991205731198790) minus 119879 (1 + 119899)(minus119879)119899 (1 minus 2120573) + 1198901205731198790119879 (119879 minus 21205731198790) minus 119879

(42)

and

Υ equiv 1 + (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + (1 minus 2120573) 120573 (minus119879)120573minus11 + 119899 (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + 119899 + 119899120573 (1 minus 2120573) (minus119879)120573minus1

(43)

6 Advances in High Energy Physics

(T)

250

300

350

400

minus1 1 2 30z

Figure 5 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573)

W(T)

minus1100minus1050

minus1minus0950minus0900minus0850minus0800minus0750minus0700minus0650minus0600minus0550minus0500

minus05 0 05 1 15 2 25 3minus1z

Figure 6 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573) where the dashlines represent 120596(119879)0 = minus103

Finally to investigate the possible realization of thephantom-like behavior in this combinedmodel by using (40)and (41) we plot 120588(119879) and 120596(119879) versus the redshift for differentvalues of 120573 We observe that the two conditions for effectivephantom mimicry (a) where the effective energy densitymust be positive and growing with time (b) the equationof state parameter should be less than minus1 are satisfied if120573 = 02 This typical behavior of 120588(119879) and 120596(119879) versus theredshift is shown in Figures 5 and 6 respectively We notethat unlike the previous two cases this model is strictly infavor of the observational data As is seen from Figure 6it is obvious that the effective equation of state parametercan cross the 120596(119879) = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1 andamount 120596(119879) for current time (119911 = 0) is consistent with theresent observational data It means that universe evolves from

quintessence-like phase towards the phantom-like phaseWe can conclude that this model is capable of realizing asuitable dynamical mechanism for getting the present timecosmic acceleration and transition to a phantom-like stagein a fascinating manner Consequently this model is morecosmologically viable than the previous two models

4 Conclusion

In this paper we have investigated possible realization ofan effective phantom behavior in some viable 119891(119879) gravitymodels With effective phantom-like behavior we mean aneffective energy density that should be positive and growingpositively with time and also the equation of state parametershould be less thanminus1We have chosen three differentmodelsof 119891(119879) gravity where two of them are reliable based onprevious studies and our third model is a combined modelWe have shown that model with 119891(119879) = 119879 + 1198910(minus119879)119901realizes an effective phantom-like behavior if 119901 = 0028As is shown in Figure 2 we obtained the effective equationof state parameter for present time about 120596(119879)0 = minus103where this amount is acceptable according to the recentdata from Planck2018 But this model evolves from effectivephantom-like phase towards the effective quintessence-likephase in future Thus this model is not in complete favorof observation since observation shows transition fromquintessence-like to phantom-like phase We have presentedanother 119891(119879) model which is 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)This 119891(119879)model realizes an effective phantom-like behaviorif 120572 = 007 Although 120596(119879)0 is obtained as an acceptable valuethat is shown in Figure 4 this 119891(119879) function is not also infavor of observation since in this model the crossing of thephantom divide could not occur and the universe evermoreis in the phantom phase Finally we have constructed a119891(119879) theory by combining the two previous models whereit only contains one model parameter 120573 This model realizesan effective phantom-like behavior if 120573 = 02 Unlike theprevious two models this model is cosmologically moreviable since the equation of state parameter in this modelevolves from effective quintessence-like phase towards aneffective phantom-like phase As is shown in Figure 6 it isobvious that 120596(119879) can cross the 120596 = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1and amount 120596(119879)0 is consistent with the resent observationaldata Therefore this combined model is in agreement withthe observational data

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

It is a pleasure to thank Professor Kourosh Nozari forhelpful discussions and valuable comments Also this work

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

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Submit your manuscripts atwwwhindawicom

4 Advances in High Energy Physics

respect by using the equations (28) and (29) Figures 1 and2 are plotted Also we have used Ω1198980 = 0315 1198670 =674119896119898119904minus1119872119901119888minus1 and ] = 195 in all numerical calculationsin the paper This value 119901 is in agreement with the resultsreported in literature In Figure 2 as we can see the effectiveequation of state parameter for the present time (119911 = 0)is 1205960 = minus103 this amount is in favor of the recent datafrom Planck2018 However we should pay attention that inthis form of 119891(119879) the effective equation of state parametercrosses the cosmological constant (phantom divide) line120596 = minus1 from phantom-like phase to the quintessence-like phase in future This behavior is not in favor of theobservational data that show transition from the quintessencephase to the phantom phase Nevertheless having a positivelygrowing energy density is a favorable capability of thismodel

32 Phantom-Like Effect with 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) Inthis model 120572 is an independent parameter and 1198790 = 119879(119911 = 0)is the current value of the torsion scalar In the limit 120572 997888rarr 0this model recovers the Λ119862119863119872 model [34] Also by usingthe modified Friedmann equation we find

120585 = minus 1 minus Ω11989801 minus (1 minus 2120572) 119890120572 (30)

In this model if 120572 gt 0 the universe has a phantom phase(with 120596 lt minus1) and if 120572 lt 0 it has a quintessence phase(with 120596 gt minus1) [48] For this form of 119891(119879) function weobtain

119865 (119879) = 120585119879 (1 minus 1198901205721198790119879) (31)

119865119879 = 1205851205721198790119879 1198901205721198790119879 + 120585 (1 minus 1198901205721198790119879) (32)

and

119865119879119879 = minus120572211987920 1205851198793 1198901205721198790119879 (33)

Once again using (20) and (21) we acquire 120588(119879) and 120596(119879) inthe present model as follows

120588(119879) = 212057212058511987901198901205721198790119879 + 119879120585 (1 minus 1198901205721198790119879)16120587119866 (34)

and

120596(119879) = minus1 + (119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879 minus 119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792))(119879120585 (1198901205721198790119879 minus 1) minus 212058512057211987901198901205721198790119879) (120585 minus 1205851198901205721198790119879 (1 minus 1205721198790119879 + 2120572211987920 1198792) + 1)

(35)

respectively We try to see possible realization of the effectivephantom-like behavior in this model by numerical treatmentof these quantities We investigated the behavior of 120588(119879) and120596(119879) versus the redshift 119911 for different choices of the modelparameter 120572 Our analysis shows that the phase of expansionof the universe (according to the values of 120596) depends onthe sign of the parameter 120572 We find that 120572 = 007 is theacceptable value for realization of an effective phantom-likebehavior in this model By using (34) and (35) the evolutionsof 120588(119879) and 120596(119879) versus the redshift are shown respectivelyin Figures 3 and 4 Figure 3 shows an increasing (positivelygrowing) energy density with the cosmic time (inverse of theredshift) In Figure 4 as we can see with the proper selectionof parameters this model can display 120596(119879) = minus103 forpresent time Also Figure 4 shows that the effective equationof state stays always less than minus1 in this model Therefore wenote that in this model the crossing of the phantom dividecould not occur and the universe evermore is in the phantomphase Similar to the previous case this behavior is not infavor of the observational data that shows transition from thequintessence phase to the phantom phase Therefore we canconclude that the present model is not observationally viable

33 Phantom-Like Effect with 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) +(minus119879)120573) The above two models have been used in the liter-atures for a variety of purposes Possible transition to the

phantom phase of the cosmic expansion has been treatedwith the mentioned 119891(119879)models in a context a little differentfrom our approach Here and for the sake of more novelty ofthe treatment we consider a combined model that containsa relatively more general 119891(119879) function This approach isintroduced in [48] The number of free parameters here ismore than the previous cases Usually with a wider parameterspace one expects to encounter more fine-tuning of theparameter to have cosmologically viable solutions But in thesame time it is easier in principle to find some subspaces ofthe model parameter space to fulfill the required expectationFor the sake of simplicity we have taken 120585 = 1198910 equiv 119899 and119901 = 120572 equiv 120573 Here 120573 and 119899 are two parameters of model only120573 is free parameter because 119899 can be obtained as

119899 = minus Ω1198980 minus 1(1 minus 2120573) (61198670)2120573minus2 + (1 minus (1 minus 2120573) 119890120573)

(36)

Also for this combined model we can acquire

119865 (119879) = 119899 (119879 minus 119879119890(1205731198790119879) + (minus119879)120573) (37)

119865119879 = 1198991205731198790119879 1198901205731198790119879 + 119899 (1 minus 1198901205731198790119879) minus 119899120573 (minus119879)120573minus1 (38)

and

119865119879119879 = minus1198991205732119879201198793 1198901205731198790119879 + 119899120573 (120573 minus 1) (minus119879)119901minus2 (39)

Advances in High Energy Physics 5

0 1 32z

068

(T)

070

072

074

076

078

080

Figure 1 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 1198910(minus119879)119901

W(T)

minus1minus2 1 2 30z

minus15

minus14

minus13

minus12

minus11

minus1

Figure 2 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 1198910(minus119879)119901 where the dash lines represent120596(119879)0 = minus103

Similar to the former two models by using (20) and (21) weobtain the effective density and equation of state parameterfor this model respectively as follows

120588(119879) = 119899 ((minus119879)120573 (2120573 minus 1) + 119879 + 1198901205731198790119879 (21205731198790 minus 119879))16120587119866 (40)

and

120596(119879) = minus1 + ΘΥ (41)

420

430

440

450

460

470

480

0 1 2 3minus1z

(T)

Figure 3 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)

1 2 30z

minus120minus119minus118minus117minus116minus115minus114minus113minus112minus111minus110minus109minus108minus107minus106minus105minus104minus103minus102minus101minus100minus099

W(T)

Figure 4 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) where the dash linesrepresent 120596(119879)0 = minus103

where we have defined

Θ

equiv 119899 (minus119879)120573 (1 minus 2120573) + 1198901205731198790119879 (119879119899 minus 21198991205731198790) minus 119879 (1 + 119899)(minus119879)119899 (1 minus 2120573) + 1198901205731198790119879 (119879 minus 21205731198790) minus 119879

(42)

and

Υ equiv 1 + (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + (1 minus 2120573) 120573 (minus119879)120573minus11 + 119899 (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + 119899 + 119899120573 (1 minus 2120573) (minus119879)120573minus1

(43)

6 Advances in High Energy Physics

(T)

250

300

350

400

minus1 1 2 30z

Figure 5 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573)

W(T)

minus1100minus1050

minus1minus0950minus0900minus0850minus0800minus0750minus0700minus0650minus0600minus0550minus0500

minus05 0 05 1 15 2 25 3minus1z

Figure 6 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573) where the dashlines represent 120596(119879)0 = minus103

Finally to investigate the possible realization of thephantom-like behavior in this combinedmodel by using (40)and (41) we plot 120588(119879) and 120596(119879) versus the redshift for differentvalues of 120573 We observe that the two conditions for effectivephantom mimicry (a) where the effective energy densitymust be positive and growing with time (b) the equationof state parameter should be less than minus1 are satisfied if120573 = 02 This typical behavior of 120588(119879) and 120596(119879) versus theredshift is shown in Figures 5 and 6 respectively We notethat unlike the previous two cases this model is strictly infavor of the observational data As is seen from Figure 6it is obvious that the effective equation of state parametercan cross the 120596(119879) = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1 andamount 120596(119879) for current time (119911 = 0) is consistent with theresent observational data It means that universe evolves from

quintessence-like phase towards the phantom-like phaseWe can conclude that this model is capable of realizing asuitable dynamical mechanism for getting the present timecosmic acceleration and transition to a phantom-like stagein a fascinating manner Consequently this model is morecosmologically viable than the previous two models

4 Conclusion

In this paper we have investigated possible realization ofan effective phantom behavior in some viable 119891(119879) gravitymodels With effective phantom-like behavior we mean aneffective energy density that should be positive and growingpositively with time and also the equation of state parametershould be less thanminus1We have chosen three differentmodelsof 119891(119879) gravity where two of them are reliable based onprevious studies and our third model is a combined modelWe have shown that model with 119891(119879) = 119879 + 1198910(minus119879)119901realizes an effective phantom-like behavior if 119901 = 0028As is shown in Figure 2 we obtained the effective equationof state parameter for present time about 120596(119879)0 = minus103where this amount is acceptable according to the recentdata from Planck2018 But this model evolves from effectivephantom-like phase towards the effective quintessence-likephase in future Thus this model is not in complete favorof observation since observation shows transition fromquintessence-like to phantom-like phase We have presentedanother 119891(119879) model which is 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)This 119891(119879)model realizes an effective phantom-like behaviorif 120572 = 007 Although 120596(119879)0 is obtained as an acceptable valuethat is shown in Figure 4 this 119891(119879) function is not also infavor of observation since in this model the crossing of thephantom divide could not occur and the universe evermoreis in the phantom phase Finally we have constructed a119891(119879) theory by combining the two previous models whereit only contains one model parameter 120573 This model realizesan effective phantom-like behavior if 120573 = 02 Unlike theprevious two models this model is cosmologically moreviable since the equation of state parameter in this modelevolves from effective quintessence-like phase towards aneffective phantom-like phase As is shown in Figure 6 it isobvious that 120596(119879) can cross the 120596 = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1and amount 120596(119879)0 is consistent with the resent observationaldata Therefore this combined model is in agreement withthe observational data

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

It is a pleasure to thank Professor Kourosh Nozari forhelpful discussions and valuable comments Also this work

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom

Advances in High Energy Physics 5

0 1 32z

068

(T)

070

072

074

076

078

080

Figure 1 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 1198910(minus119879)119901

W(T)

minus1minus2 1 2 30z

minus15

minus14

minus13

minus12

minus11

minus1

Figure 2 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 1198910(minus119879)119901 where the dash lines represent120596(119879)0 = minus103

Similar to the former two models by using (20) and (21) weobtain the effective density and equation of state parameterfor this model respectively as follows

120588(119879) = 119899 ((minus119879)120573 (2120573 minus 1) + 119879 + 1198901205731198790119879 (21205731198790 minus 119879))16120587119866 (40)

and

120596(119879) = minus1 + ΘΥ (41)

420

430

440

450

460

470

480

0 1 2 3minus1z

(T)

Figure 3 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)

1 2 30z

minus120minus119minus118minus117minus116minus115minus114minus113minus112minus111minus110minus109minus108minus107minus106minus105minus104minus103minus102minus101minus100minus099

W(T)

Figure 4 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879) where the dash linesrepresent 120596(119879)0 = minus103

where we have defined

Θ

equiv 119899 (minus119879)120573 (1 minus 2120573) + 1198901205731198790119879 (119879119899 minus 21198991205731198790) minus 119879 (1 + 119899)(minus119879)119899 (1 minus 2120573) + 1198901205731198790119879 (119879 minus 21205731198790) minus 119879

(42)

and

Υ equiv 1 + (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + (1 minus 2120573) 120573 (minus119879)120573minus11 + 119899 (1205731198790119879 minus 2120573211987920 1198792 minus 1) 1198901205731198790119879 + 119899 + 119899120573 (1 minus 2120573) (minus119879)120573minus1

(43)

6 Advances in High Energy Physics

(T)

250

300

350

400

minus1 1 2 30z

Figure 5 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573)

W(T)

minus1100minus1050

minus1minus0950minus0900minus0850minus0800minus0750minus0700minus0650minus0600minus0550minus0500

minus05 0 05 1 15 2 25 3minus1z

Figure 6 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573) where the dashlines represent 120596(119879)0 = minus103

Finally to investigate the possible realization of thephantom-like behavior in this combinedmodel by using (40)and (41) we plot 120588(119879) and 120596(119879) versus the redshift for differentvalues of 120573 We observe that the two conditions for effectivephantom mimicry (a) where the effective energy densitymust be positive and growing with time (b) the equationof state parameter should be less than minus1 are satisfied if120573 = 02 This typical behavior of 120588(119879) and 120596(119879) versus theredshift is shown in Figures 5 and 6 respectively We notethat unlike the previous two cases this model is strictly infavor of the observational data As is seen from Figure 6it is obvious that the effective equation of state parametercan cross the 120596(119879) = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1 andamount 120596(119879) for current time (119911 = 0) is consistent with theresent observational data It means that universe evolves from

quintessence-like phase towards the phantom-like phaseWe can conclude that this model is capable of realizing asuitable dynamical mechanism for getting the present timecosmic acceleration and transition to a phantom-like stagein a fascinating manner Consequently this model is morecosmologically viable than the previous two models

4 Conclusion

In this paper we have investigated possible realization ofan effective phantom behavior in some viable 119891(119879) gravitymodels With effective phantom-like behavior we mean aneffective energy density that should be positive and growingpositively with time and also the equation of state parametershould be less thanminus1We have chosen three differentmodelsof 119891(119879) gravity where two of them are reliable based onprevious studies and our third model is a combined modelWe have shown that model with 119891(119879) = 119879 + 1198910(minus119879)119901realizes an effective phantom-like behavior if 119901 = 0028As is shown in Figure 2 we obtained the effective equationof state parameter for present time about 120596(119879)0 = minus103where this amount is acceptable according to the recentdata from Planck2018 But this model evolves from effectivephantom-like phase towards the effective quintessence-likephase in future Thus this model is not in complete favorof observation since observation shows transition fromquintessence-like to phantom-like phase We have presentedanother 119891(119879) model which is 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)This 119891(119879)model realizes an effective phantom-like behaviorif 120572 = 007 Although 120596(119879)0 is obtained as an acceptable valuethat is shown in Figure 4 this 119891(119879) function is not also infavor of observation since in this model the crossing of thephantom divide could not occur and the universe evermoreis in the phantom phase Finally we have constructed a119891(119879) theory by combining the two previous models whereit only contains one model parameter 120573 This model realizesan effective phantom-like behavior if 120573 = 02 Unlike theprevious two models this model is cosmologically moreviable since the equation of state parameter in this modelevolves from effective quintessence-like phase towards aneffective phantom-like phase As is shown in Figure 6 it isobvious that 120596(119879) can cross the 120596 = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1and amount 120596(119879)0 is consistent with the resent observationaldata Therefore this combined model is in agreement withthe observational data

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

It is a pleasure to thank Professor Kourosh Nozari forhelpful discussions and valuable comments Also this work

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom

6 Advances in High Energy Physics

(T)

250

300

350

400

minus1 1 2 30z

Figure 5 Variation of the effective energy density versus the redshiftfor 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573)

W(T)

minus1100minus1050

minus1minus0950minus0900minus0850minus0800minus0750minus0700minus0650minus0600minus0550minus0500

minus05 0 05 1 15 2 25 3minus1z

Figure 6 Variation of effective equation of state parameter versusthe redshift for 119891(119879) = 119879 + 119899(119879 minus 119879119890(1205731198790119879) + (minus119879)120573) where the dashlines represent 120596(119879)0 = minus103

Finally to investigate the possible realization of thephantom-like behavior in this combinedmodel by using (40)and (41) we plot 120588(119879) and 120596(119879) versus the redshift for differentvalues of 120573 We observe that the two conditions for effectivephantom mimicry (a) where the effective energy densitymust be positive and growing with time (b) the equationof state parameter should be less than minus1 are satisfied if120573 = 02 This typical behavior of 120588(119879) and 120596(119879) versus theredshift is shown in Figures 5 and 6 respectively We notethat unlike the previous two cases this model is strictly infavor of the observational data As is seen from Figure 6it is obvious that the effective equation of state parametercan cross the 120596(119879) = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1 andamount 120596(119879) for current time (119911 = 0) is consistent with theresent observational data It means that universe evolves from

quintessence-like phase towards the phantom-like phaseWe can conclude that this model is capable of realizing asuitable dynamical mechanism for getting the present timecosmic acceleration and transition to a phantom-like stagein a fascinating manner Consequently this model is morecosmologically viable than the previous two models

4 Conclusion

In this paper we have investigated possible realization ofan effective phantom behavior in some viable 119891(119879) gravitymodels With effective phantom-like behavior we mean aneffective energy density that should be positive and growingpositively with time and also the equation of state parametershould be less thanminus1We have chosen three differentmodelsof 119891(119879) gravity where two of them are reliable based onprevious studies and our third model is a combined modelWe have shown that model with 119891(119879) = 119879 + 1198910(minus119879)119901realizes an effective phantom-like behavior if 119901 = 0028As is shown in Figure 2 we obtained the effective equationof state parameter for present time about 120596(119879)0 = minus103where this amount is acceptable according to the recentdata from Planck2018 But this model evolves from effectivephantom-like phase towards the effective quintessence-likephase in future Thus this model is not in complete favorof observation since observation shows transition fromquintessence-like to phantom-like phase We have presentedanother 119891(119879) model which is 119891(119879) = 119879 + 120585119879(1 minus 1198901205721198790119879)This 119891(119879)model realizes an effective phantom-like behaviorif 120572 = 007 Although 120596(119879)0 is obtained as an acceptable valuethat is shown in Figure 4 this 119891(119879) function is not also infavor of observation since in this model the crossing of thephantom divide could not occur and the universe evermoreis in the phantom phase Finally we have constructed a119891(119879) theory by combining the two previous models whereit only contains one model parameter 120573 This model realizesan effective phantom-like behavior if 120573 = 02 Unlike theprevious two models this model is cosmologically moreviable since the equation of state parameter in this modelevolves from effective quintessence-like phase towards aneffective phantom-like phase As is shown in Figure 6 it isobvious that 120596(119879) can cross the 120596 = minus1 line at 05 lt 119911119888119903119900119904119904 lt 1and amount 120596(119879)0 is consistent with the resent observationaldata Therefore this combined model is in agreement withthe observational data

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

It is a pleasure to thank Professor Kourosh Nozari forhelpful discussions and valuable comments Also this work

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom

Advances in High Energy Physics 7

has been supported financially by Research Institute forAstronomy and Astrophysics of Maragha (RIAAM) underresearch project number 16025-64

References

[1] S Perlmutter G Aldering and G Goldhaber ldquoMeasurementsofΩ andΛ from42 high-redshift supernovaerdquoTheAstrophysicalJournal vol 517 no 2 pp 565ndash586 1999

[2] A G Riess L-G Sirolger J Tonry et al ldquoType Ia supernovadiscoveries at zgt1 from theHubble Space Telescope evidence forpast deceleration and constraints on dark energy evolutionrdquoTheAstrophysical Journal vol 607 no 2 pp 665ndash687 2004

[3] G Hinshaw C Barnes C L Bennett et al ldquoThree-yearwilkinson microwave anisotropy probe (WMAP) observationstemperature analysisrdquo The Astrophysical Journal SupplementSeries 2007

[4] G Hinshaw D Larson E Komatsu et al ldquoNine-year wilkinsonmicrowave anisotropyprobe (WMAP)observations cosmolog-ical parameter resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[5] C L Bennett D Larson J L Weiland et al ldquoNine-yearwilkinson microwave anisotropy probe (WMAP) observationsfinalmaps and resultsrdquoAstrophysics Cosmology andNongalacticAstrophysics 2012

[6] M Tegmark M Strauss M Blanton et al ldquoCosmologicalparameters from SDSS and WMAPrdquo Physical Review D Parti-cles Fields Gravitation andCosmology Article ID 103501 2004

[7] S P Boughn andRG Crittenden ldquoA detection of the integratedSachs-Wolfe effectrdquo New Astronomy Reviews vol 49 no 2 pp75ndash78 2005

[8] P A R Ade N Aghanim C Armitage-Caplan et al ldquoPlanck2013 results XVI Cosmological parametersrdquoAstrophysics Cos-mology and Nongalactic Astrophysics 2013

[9] N Aghanim Y Akrami M Ashdown et al ldquoPlanck 2018results VI Cosmological parametersrdquo Astrophysics Cosmologyand Nongalactic Astrophysics 2018

[10] J Weller ldquoBubbles from dark energyrdquo Astrophysics 2000[11] E J Copeland M Sami and S Tsujikawa ldquoDynamics of dark

energyrdquo International Journal of Modern Physics D GravitationAstrophysics Cosmology vol 15 no 11 pp 1753ndash1935 2006

[12] Y F Cai E N Saridakis M R Setare and J Xia ldquoQuintomcosmology theoretical implications and observationsrdquo PhysicsReports vol 493 no 1 pp 1ndash60 2010

[13] A De Felice and S J Tsujikawa ldquof(R) theoriesrdquo Living Reviewsin Relativity vol 13 p 3 2010

[14] S Nojiri and S D Odintsov ldquoUnified cosmic history inmodified gravity from F(R) theory to Lorentz non-invariantmodelsrdquo Physics Reports vol 505 pp 59ndash144 2011

[15] S Nojiri and S D Odintsov ldquoModifiedGaussndashBonnet theory asgravitational alternative for dark energyrdquo Physics Letters B vol631 no 1-2 pp 1ndash6 2005

[16] A De Felice and S Tsujikawa ldquoConstruction of cosmologicallyviable f(G) dark energy modelsrdquo Physics Letters B vol 675 no1 pp 1ndash8 2009

[17] C de Rham ldquoMassive gravityrdquo Living Reviews in Relativity vol17 no 7 2014

[18] N Deruelle and L Farina-Busto ldquoLovelock gravitational fieldequations in cosmologyrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 41 no 12 pp 3696ndash3708 1990

[19] P Horava ldquoMembranes at quantum criticalityrdquo Journal of HighEnergy Physics vol 2009 article 020 2009

[20] K Nozari ldquoDGP cosmology with a non-minimally coupledscalar field on the branerdquo Journal of Cosmology andAstroparticlePhysics no 9 2007

[21] K Hayashi and T Shirafuji ldquoNew general relativityrdquo PhysicalReview D Particles Fields Gravitation and Cosmology vol 19no 12 pp 3524ndash3553 1979

[22] A Unzicker and T Case ldquoTranslation of Einsteins attempt of aunified field theorywith teleparallelismrdquoHistory and Philosophyof Physics 2005

[23] G Y Chee Y Zhang and Y Guo ldquoGravitational energy-momentumand theHamiltonian formulation of the teleparallelgravityrdquo General Relativity and Quantum Cosmology 2001

[24] R Aldrovandi and J G Pereira Teleparallel Gravity An Intro-duction vol 173 Springer New York NY USA 2013

[25] J W Maluf ldquoThe teleparallel equivalent of general relativityrdquoAnnalen der Physik vol 525 no 5 pp 339ndash357 2013

[26] G R Bengochea and R Ferraro ldquoDark torsion as the cosmicspeed-uprdquo Physical Review D Particles Fields Gravitation andCosmology vol 79 no 12 Article ID 124019 5 pages 2009

[27] P Wu and H Yu ldquoThe dynamical behavior of f(T) theoryrdquoPhysics Letters B vol 692 pp 176ndash179 2010

[28] J B Dent S Dutta and E N Saridakis ldquof(T) gravitymimickingdynamical dark energy Background and perturbation analysisrdquoJournal of Cosmology and Astroparticle Physics vol 2011 2011

[29] S M Carroll ldquoThe cosmological constantrdquo Living Reviews inRelativity vol 4 article 1 2001

[30] T Padmanabhan ldquoCosmological constantmdashthe weight of thevacuumrdquo Physics Reports vol 380 no 5-6 pp 235ndash320 2003

[31] K Nozari R Shojaee and S Karimzadeh ldquoInterpretationof rotation curves of spiral galaxies in modified teleparallelgravityrdquo Communications in Theoretical Physics vol 60 no 6pp 687ndash690 2013

[32] A Behboodi S Akhshabi and K Nozari ldquoBraneworld setupand embedding in teleparallel gravityrdquo Physics Letters B Parti-cle Physics Nuclear Physics and Cosmology 2014

[33] F Kiani and K Nozari ldquoEnergy conditions in F(T Θ) gravityand compatibilitywith a stable de Sitter solutionrdquoPhysics LettersB 2014

[34] Y-F Cai S Capozziello M De Laurentis and E N SaridakisldquoF(T) teleparallel gravity and cosmologyrdquo Reports on Progress inPhysics vol 79 no 04 2016

[35] R CNunes ldquoStructure formation in119891(119879) gravity and a solutionfor1198670 tensionrdquo Journal of Cosmology and Astroparticle Physicsvol 05 no 052 2018

[36] G G L Nashed and E N Saridakis ldquoRotating AdS black holesin Maxwell-f(T)gravityrdquoHigh Energy Physics - Theory 2018

[37] U Debnath ldquoCharge gravastars in f(T) modified gravityrdquoGeneral Relativity and Quantum Cosmology 2019

[38] R C Nunes S Pan and E N Saridakis ldquoNew observationalconstraints on f(T) gravity from cosmic chronometersrdquo Journalof Cosmology and Astroparticle Physics vol 2016 no 08 articleno 011 2016

[39] R C Nunes A Bonilla S Pan and E N Saridakis ldquoObser-vational constraints on f(T) gravity from varying fundamentalconstantsrdquoThe European Physical Journal C vol 77 no 4 2017

[40] L P Chimento R Lazkoz RMaartens and IQuiros ldquoCrossingthe phantom divide without phantom matterrdquo Journal of Cos-mology and Astroparticle Physics no 9 2006

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom

8 Advances in High Energy Physics

[41] V Sahni and Y Shtanov ldquoBraneworld models of dark energyrdquoJournal of Cosmology and Astroparticle Physics vol 11 article014 2003

[42] V Sahni ldquoCosmological surprises from braneworld models ofdark energyrdquoGeneral relativity and Gravitation 2005

[43] A Lue and G D Starkman ldquoHow a brane cosmologicalconstant can trick us into thinking that w lt -1rdquo Physical ReviewD Particles Fields Gravitation and Cosmology vol 70 no 10pp 1ndash101501 2004

[44] K Nozari and M Pourghasemi ldquoCrossing the phantom divideline in a Dvali-Gabadadze-Porrati-inspired F(R120593) gravityrdquoJournal of Cosmology and Astroparticle Physics vol 2008 no10 2008

[45] K Nozari and T Azizi ldquoPhantom-like effects on warped DGPbranerdquoCommunications inTheoretical Physics vol 54 no 4 pp773ndash780 2010

[46] K Nozari and N Alipour ldquoPhantom mimicry on the normalbranch of a dgp-inspired braneworld scenario with curvatureeffectrdquoModernPhysics Letters A vol 25 no 3 pp 189ndash210 2010

[47] K Nozari and T Azizi ldquoPhantom-Like in f(R) Gravityrdquo PhysicsLetters B vol 608 no 205 2009

[48] K Bamba C-Q Geng C-C Lee and L-W Luo ldquoEquation ofstate for dark energy in f(T) gravityrdquo Journal of Cosmology andAstroparticle Physics vol 2011 no 1 2011

[49] R-J Yang ldquoNew types of 119891(119879) gravityrdquo The European PhysicalJournal C vol 71 Article ID 1797 2011

[50] P Wu and H Yu ldquoObservational constraints on f(T) theoryrdquoPhysics Letters B 2010

[51] C-Q Geng C-C Lee E N Saridakis and Y-P WuldquolsquoTeleparallelrsquo dark energyrdquo Physics Letters B vol 704 no 5 pp384ndash387 2011

[52] A Behboodi S Akhshabi and K Nozari ldquoMatter stability inmodified teleparallel gravityrdquo Physics Letters B vol 718 no 302012

[53] A Paliathanasis J D Barrow and P G Leach ldquoCosmologicalsolutions of 119891(119879) gravityrdquo Physical Review D Particles FieldsGravitation and Cosmology vol 94 no 2 Article ID 023525 10pages 2016

[54] Y-F Cai T Qiu Y-S Piao M Li and X Zhang ldquoBouncinguniverse with quintom matterrdquo Journal of High Energy Physicsvol 0710 no 071 2007

[55] S Nesseris S Basilakos E N Saridakis and L Perivolaropou-los ldquoViable f(T) models are practically indistinguishable fromLCDMrdquo Physical Review D Particles Fields Gravitation andCosmology vol 88 no 10 Article ID 103010 2013

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

AstronomyAdvances in

Antennas andPropagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal of

Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom