Direct Evidence of acceleration from Direct Evidence of acceleration from a distance modulus-redshift grapha distance modulus-redshift graph

Yungui Gong 龚云贵

College of Mathematics and Physics

Chongqing University of Posts and Telecommunications

重庆邮电大学数理学院

String Theory and Cosmology Workshop ， KITPC, 10/22/2007

OutlinesOutlinesIntroductionSN Ia EvidenceIntroduction to numerical Fitting Dark Energy ParameterizationConclusion

Dark EnergyDark Energy

Quintessence?Quintessence?

Dark EnergyDark Energy

Type Ia Supernova Type Ia Supernova ObservationObservationObservational Data: Redshift-Luminosity distance

For a given cosmological model, calculate Luminosity distance-redshift relation

To fit observation data, need to assume a model and then fit the parameters in the model

Dark EnergyDark Energy

SN Ia EvidenceSN Ia Evidence

Model: Cosmological constantModel independent Way? Energy Condition

Friedmann EquationFriedmann Equation

Friedmann Equation

0)(3

)3(3

43

82

2

pH

pG

a

a

G

a

kH

Acceleration and Energy Acceleration and Energy ConditionsConditions

Energy Conditions in Distance Energy Conditions in Distance graphgraphStrong Energy Condition

03 p

0 p

Results?Results?The SEC was first violated billions of

years ago, at z~1.1 (Santos etal., PRD 74 (06) 067301; PRD 75(07) 083523 ） .

03 p

CDM ModelCDM ModelDeceleration to Acceleration

Transition happened at z<0.8

How to interpret? How to interpret? Gong and Wang, JCAP 0708 (07)

018; PLB 652 (07) 63Key Points: SEC and the derived

luminosity conditions are not equivalent!

ReasonsReasonsIntegration Effect

Key PointsKey Points

SEC leads to upper bound on the luminosity distance

Violation of the upper bound means violation of SEC

Violation of the upper bound at z does not necessarily mean the violation of SEC at the same z

Satisfaction of the upper bound up to z does not mean no violation of SEC up to z

)1ln()1()(03 0 zzzdHp L

ConclusionConclusionEnergy condition can

be used to give direct and model-independent evidence of cosmic acceleration

No detailed information about the acceleration can be given

No information on dark energy can be given

Parameter DegeneracyParameter Degeneracy

At Low Red-shift (z<0.1), Almost the same (z)–z relation

To the first order, w(z=0)

zHzdL )( 0

Numerical FittingNumerical FittingFor a given cosmological model, we can calculate

the luminosity distance (or distance modulus) with given parameters P

Find out the parameters that gives the minimum value of

Parameter space: grid (point to point search), Monte Carlo Markov Chain method

)|( PzdL)|( Pz

2

22 -)|(

obsPz

Toy Model (Essence Data)Toy Model (Essence Data)

85.043.1 :3

59.0,12.1 ,17.195

0

02

w

ww a

c

a

c z

w

z

www

110

2

1.0 ,59.0 ,12.10 ca zww

88.196,4.0)0(

12.196,0.2)0(2

1

21

zww

zww

The error of The error of ww((zz=0)=0)

The sweet spotThe sweet spot

结论结论

Energy condition can be used to give direct and model-independent evidence of cosmic acceleration

The luminosity distance is almost independent of cosmological models at low redshift, so the value of w(z=0) may not be well determined.

Thank youThank you！！