Holographic and agegraphic dark energy models

Yun Soo Myung Inje University, Gimhae, Korea

Contents

1. Introduction2. Sourced Friedmann equations3. Interacting holographic dark energy model4. Agegraphic dark energy model5. New agegraphic dark energy model6. Discussions

1. Introduction

model CDMmodelcosmology Present

1 with matter dunclustere :energy)DE(dark

0th matter wi clustered:matter)dark CDM(cold

parameter;density :/

%)73(%)23(%)4(

03.0-1

flat. is universe that thepredictsInflation

]98011[state) ofon EOS(equati

06.004.1 EOS with UngAccelerati Ia SN

Cosmology. Standard FRW UInflation

c

w

w

.,-.-

pw

DECDMBmtot

tot

o

Introduction

Main issue of the present cosmology:How to explain the present accelerating universe? Candidates for DE with w<-1/3 1) cosmological constant (w=-1) 2) quintessence (w>=-1) 3) K-essence (w>=-1) 4) holographic dark energy (w>=-1) 5) phantom matter (w<-1)Can we rule out a dynamical DE model?Can we rule out the phantom phase of w<-1?

phantom matter violates all the energy conservation laws.

Introduction

Dark energy a repulsive form of

gravity in space present 9 billion years ago. its effect becomes more

dominant as the universe expands.

Einstein the first person to realize that the empty space is not the space as nothingness.

introduce the cosmological constant to balance the universe against the inward pull of its own gravity.

Introduction-cosmological constant

model "constant alcosmologic dynamical" a need WeSolution 8

3density energy scalePlanck with compared when

small very veryis 10 8

3density criticalPresent

problem tuningFine

QFT of in viewdensity energy Vacuum8

3 :energydark a asconstant alCosmologic

4

p

p122

20

2

c

2

p

-p

pV

M

HM

M

Introduction-another models

32

21

not but LL

M p 1)1) Holographic dark energy densityHolographic dark energy density

2) Vacuum fluctuation energy density 2) Vacuum fluctuation energy density

3) Geometric mean of 3) Geometric mean of

4) Casimir energy of QM4) Casimir energy of QM

5) Uncertainty of 5) Uncertainty of

distance in holographic form cosmologydistance in holographic form cosmology

6) Entanglement energy?6) Entanglement energy?------------------------------------------------------------------

2),3)Astro-ph/0411044,2),3)Astro-ph/0411044,

4)gr-qc/0405111, 5) PLB469,2434)gr-qc/0405111, 5) PLB469,243

cp3L

EV

23/12 )1

()(p

p

Introduction-HDEM

2

2

BH

2433

223

holeblack size-system ofdensity energy

: (HDE)density energy cHolographi

:boundEnergy

4)( :boundEntropy

:bounds twohave we

cutoff IR and th UVgravity wi including systemFor

gravity mechanics Quantumon based

(HDEM) modelenergy dark cHolographi

L

M

LMMLLE

MLG

ASLS

L

p

pBH

pBH

Introduction-gravitational holography

**Gravitational Holography limits number of states accessible to a system including gravity.

**Considering an infinite contribution to the vacuum energy is not correct when the gravity is present.

**Projection from states in bulk-volume to states on covering surface holographic principle.

Introduction-HDEM

Ungaccelerati

)/(/ with (FEH)horizon event future 3)

Ungdecelerati

)/(/ with (PH)horizon particle 2)

EOSfor N/A

horizon Hubble/1 )1

universe theof size cutoff IR

parameter with 8

3 :HDE of formA

2

2

0 0

2

22

HadaaadtaRRL

HadaaadtaRRL

HL

L

cL

Mc

t a

FHFH

t a

PHPH

p

2. Sourced Friedmann equations

Qqq

dtqdtqM

H

k

L

Mcpp

MH

k

wpqpH

wpqpH

tt

mp

pmm

p

mmmmmm

21

0

2

0

122

2

22

2

02

01

if Eq,Friedmann first

}{3

8

1 with EqFriedmann Sourced

8

3 with }{

4

1 with Eq Friedmann Second

)(3

,)(3

HDEM and CDMfor Equations continuity Two

Sourced Friedmann equations

nsferenergy traexplain tomechanism cmicroscopi a need We

and : EOS effective define tohave We

and toaccording evolvenot do and

matters obetween twnsfer energy tra

matters cholographi andordinary between n Interactio

equations cMacroscopi

Comments

00

effm

eff

mm

ww

ww

Macroscopic mechanism for energy transfer in two-fluid model

0}3/1{3

;0}3/1{3

:fluids imperfect edissipativ two equations continuity two

,

pressures mequilibriu-non effective large gIntroducin

ratedecay with CDM into HED of decaying

/ with /

1 with HED& 0 with CDM

0

m

21

00

mm

mm

m

HrH

HwH

H

r rQqq

ww

B

BmvFe

B

ii

t coefficien frictional-anti cosmic a is rateDecay

friction) of law sStokes'(

motion ofequation ith w

model gas ginteractin -self a introduces one if

, possible is 3h tion witinterpreta cMicroscopi

Microscopic mechanism for energy transfer in two-fluid model

3. Interacting holographic dark energy model

/)1( and 1th wi

3/8 ;3/8

parametersdensity Two

3/ ;3/

state of equations effective Two

}1

1{2

3

EqFriedmann Second

)1(3 },3

)1({3

/ with equations continuity Two

2222

0

02

20

r

HMHM

HrwHww

r

wHH

HrbHr

rwHrr

r

m

pmmp

effm

eff

m

Interacting holographic dark energy model

1 ,

3

2

3

1

valuesinitialdifferent start with twovariable,For

3

2

3

1

1 const,For

}1

321{)1(

ln with EqEvolution

3

2

3

1 EOS

22

0

2

2

2

0

bw

c

bww

r

c

bwwr

b

cdx

d

ax

b

cw

effm

eff

effm

eff

Interacting holographic dark energy model –density parameters

Interacting holographic dark energy model – effective EOS

Non-interacting holographic dark energy model-EOS

Interacting holographic dark energy model – comments

EOS. effective using when

model HDE ginteractinin phase phantom No

9.00.0 ;9.00.1

case ginteractin toginteractin-non from EOS Changing

2.00.0 ;8.00.1

case ginteractin toginteractin-non from & Changing

effmm

eff

m

m

wwww

After a long decaying, two are the new same fluid like cosmologicalAfter a long decaying, two are the new same fluid like cosmologicalconstant.constant. It seems that there is no mechanism to generate a phantom phaseIt seems that there is no mechanism to generate a phantom phase by turning on an interaction between two fluids.by turning on an interaction between two fluids.

Two quantities for the cosmological evolution : EOS and squared speed of sound velocity (SSV)

2) SSV evaluated to 0th order determines

the stability of background evolution:

p

d

dpvs 2

: stability of a first-order perturbation

)ln (0 xk0

2 axev ixikkq

: instability of a first-order perturbation

kkk aHkvv

xttxt

2222 )/("

),()(),(

xk0

2 0 ix

kkq ev

3) Linear perturbation3) Linear perturbation::

1) EOS determines the nature of background evolution1) EOS determines the nature of background evolution

EOS and SSV for HDEM

c=0.8 c=1 c=1.2

FEH

PH

blow up and phantom phase

unstable

unstable

EOS and SSV for Chaplygin gas and tachyon models

Chaplygin gas model-stable Tachyon model-stable

4. Agegraphic dark energy model (ADEM)

The Karolyhazy relation:

‘

3/13/2 ttt p

The time-energy uncertainty in the Minkowiski spacetime:

2

2

31 ~

)(~~

3

3

t

m

t

EtE pt

qt

Vacuum energy density with the parameter :

2

223

T

mn pq

universe theof age the: ' 0t

dtT

• No causality problem.

• Problem for describing the matter-dominated universe

in the par fast.

n

ADEM:non-interacting case

The first Friedmann equation:

3

12

22

mqpm

Ha

a

03

0)(3

mm

qqq

H

pH

continuity equation:

density parameter: 22

2

TH

nq 1 mq

Pressure: axdx

dp q

qq ln ,

3

1

EOS:n

p q

q

qq 3

21

The evolution equation: )1(3' qqqq

q H

SSV: q

qq

qq

q

qq

nHv

)1(9

'

)1(32

ADEM: non-interacting case

Result of ADEM (solidEOS, dashedSSV)

n=0.9 n=1.2 n=2.0

0 0)1( 10 2 qqq v-

No dark energy-dominated universe in the far future.

1 , 1 qq

for n=0.9 (n<1.0), no phantom phase of . 1q

QH

QpH

mm

qqq

3

)(3

continuity equation:

The evolution equation: , 3

)1(3'32

Hm

Q

H pqq

qq

EOS:q

q

q

qq H

Q

n

p

33

2

3

1

SSV: qeffq

qqv

)1(32

qq

effq

qq

qq H

Q

H

Q

n

3 and

33

''

with

qq HQ 3ADEM: interacting case with ADEM: interacting case with

Interacting case using EOS (solidEOS, dashedSSV)

n=0.9 n=2.0

1.0

18.0

8.0

: phantom phase1 ,0 10 2 qqq v

n=1.2

SSV:q

qeffq

effqeff

q

effq

qn

v

3

')'( ,

)1(3

)'(2

q

effq n

3

21 Effective EOS:

: no phantom phase1

),8.0 and 9.0exept ( 0 10 2

effq

qq nv

When using effective EOS, we find no phantom phase

5. New agegraphic dark energy model (NADEM)

2

223

p

q

mn

timeconformal : ')'(

'

'

'

02

0

at

Ha

da

a

dt

Vacuum energy density:

• No causality problem.

• Resolving problem for describing the matter-dominated universe

in the par fast.

NADEM: non-interacting case with matter-dominated universe

3

1)3(

2

1

)1(32

nnn

n

nn H

pv

EOS:x

n

x

nn ean

e

na

,3

21

3

21

The evolution equation: )1(3' nnnn

Evolution is nontrivial because EOS is function of x and . n

SSV SSV ::

Result of NADEM

whole evolution depends on the parameter critically.n

For EOS,n=2.6nc=2.6878 n=2.7

Region of evolution

Considering the connection between x and z :

Hence our region from x=-20( ) to x=20 ( ) covers the whole

region of evolution.

)1(ln zx

}.0,3{ toscorrespond }0,20{ xz

0a

a

far past : : non-acceptablecnn )0 and ,( 2 nnn v

cnn 22 0 and 1 ,1: a-v nnnn

cnn )1 and 3/2( universe dominatedmatter: mn

far future : for all n, 1 and 3/2 ,1 2 nnn v

The squared speed is always negative for cnn

Result of NADEM

NADEM with matter-and radiation- dominated universes

04

0)(3

rr

nnn

H

pH

continuity equation:

The evolution equation: )1(3'

,)1(3'

rrnrr

nnrnn

3

1)1(3

6

1

)1(32

nnnrn

n

nn H

pv

SSV:

Result of NADEM

far past : radiation-dominated universe

3/1 ,For 2 nc vnn 0 ,1 and 3/1 nrn

far future : dark energy –dominated universe( )1 ,1 nn

For EOS, n=2.513775 nc=2.5137752 n=2.513776

Interacting case of NADEM with

QH

QpH

mm

nnn

3

)(3

continuity equation:

The evolution equation: , 33

21)1(3'

32

Hm

Q

n

e

pn

x

nnn

EOS:n

nx

n H

Q

n

e

33

21

SSV: neffn

nn H

v

)1(32

nq

effn

nn

x

n

nn H

Q

H

Q

n

e

n

3 and

33

2

3

'

with

nHQ 3

Result- No simulation

The evolution of the native EOS and the SSV are similar to

NADEM except including the phantom phase.

When using effective EOS, we expect that

No phantom phase.

the whole evolution of the universe implies negative squared speed.

6. Discussions

Comparison between NADEM and HDEM

NADEM HDEM RemarkFar past

Far

future

Matter-dominated U

Dark energy

-dominated U

cnn nnv for )0(3

2 2

navnn llfor )3/2(1 2

cvn allfor 3

12

1for 12 cvn

The squared speed for ADEM is always negative,

so it is classically unstable like HDEM with future event horizon.

The NADEM is no better than the HDEM

for the description of the dark energy-dominated universe.

Discussions

SimilarityHDEM with particle horizon ADEMHDEM with future event horizon NADEMCommentFor n>nc, NADEM could describeMatter (radiation)-dominated Universe.