Theoretical Aspects of Dark Energy Models

Rong-Gen Cai

Institute of Theoretical Physics

Chinese Academy of Sciences

CCAST, July 4, 2005

Cosmic Acceleration?

Dynamics equations:

2 83

4 ( 3 )3

GHa G pa

π ρπ ρ

=

=− +&&

/ 3p ρ< −

(Violate the Strong Energy Condition: exotic energy component)

Dark Energy? Observation Data

Theoretical Assumptions

General Relativity Cosmo Principle

G 8∂GT (Ë )μν μν=

Model I Model II Model III

Model I: Modifications of Gravitational Theory

1) GR’s testUV: ~ 1 mm

IR: ~ solar scale

2) Modify GR

UV: quantum gravity effect

IR: cosmos scale

Brane World Scenario

Modifying GR in IR:

1) “ Ghost Condensation and a Consistent Infrared Modification of Gravity” by N. arkani-Hamed et al, hep-th/0312099,JHEP 0405 (2004) 074.

Consider a ghost field with a wrong-sign kinetic term:

Suppose the scalar field has a constant velocity:

The low-energy effective action for the fluctuation has an usual form:

2) “ Is Cosmic Speed-up due to New Gravitational Physics ” by S. M. Carroll et al. astro-ph/0306438, Phys.Rev. D70 (2004) 043528

Consider a modification becoming important at extremely low curvature

Making a conformal transformation yields a scalar field with potential:

(1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity

General case:

4 2( 1)n

nR Rμ μ +

→

More general case: hep-th/0410031, PRD71:063513,2005

Consider:

3) Brane World Scenario:

y

X μ1) N. Arkani-Hamed et al, 1998 factorizable product

2) L. Randall and R. Sundrum, 1999 warped product in AdS_5

4 x nM T

RS1:

RS2:

14 2

4

x S / x R

cM ZcM

3) DGP model, 2000 a brane embedded in a Minkovski space

a) A popular model: RS scenario

5 5

5 41 15 5 416 8( 2 ) ( )G GS d x g R d x g Kπ π σ= − − Λ − − −∫ ∫

2 242 3 44 5

8 4( ) ( )3 3 3

HM M aπ π ερ ρΛ

= + + +

where2

4 53 35 5

25

4 5

4 4( )3

3 ( )4

M M

MM M

π π σ

π σ

Λ = Λ +

=

= 0

Fine-Tuning

2) “Dark Energy” on the brane world scenario

“Braneworld models of dark energy” by V. Sahni and Y. Shtanov, astro-ph/0202346, JCAP 0311 (2003) 014

When m=0:

In general they have two branches:

Current value of the effective equation of state of “dark energy”

The acceleration can be a transient phenomenon: Brane 2

However, w crosses –1, the phantom divide? D. Huterer and A. Cooray, astro-ph/040462; Phys.Rev. D71 (2005) 023506

“Crossing w=-1 in Gauss-Bonnet Brane World with Induced Gravity ” by R.G. Cai,H.S. Zhang and A. Wang, hep-th/0505186

Consider the model

The equations of motion:

The effective equation of state of “dark energy”:

Where the Gauss-Bonnet term in the bulk and bulk mass play a curial role.

Model III: Back Reaction of Fluctuations

“Cosmological influence of super-Hubble perturbations” by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, astro-ph/0410541;

“Primordial inflation explains why the universe is accelerating today”by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, hep-th//0503117;

“On cosmic acceleration without dark energy” by E.W. Kolb, S. Matarrese, and A. Riotto, astro-ph/0506534

Inflation produces super-horizon perturbations!

Consider the presence of cosmic perturbations,

Split the gravitational potential to two parts

A local observer within the Hubble volume will see

:1/ 2 1q → −

cosmologicalconstant

which indicates the SHCDM with is indistinguishable from LCDM model.

Another scenario:

Beyond the super-horizon mode’s cut-off, the bulk universe is

There is a super-horizon sized underdense bubble containing the observable universe, with matter density equal to the average matterdensity we measure locally

Model II: Various Dark Energy Models: Acts as Source of E’eq

G 8∂GT (Ë )μν μν=

(1) Cosmological constant: w=-1

(2) Holographic energy

(3) Quintessence: -1<w<0

(4) K-essence: -1 <w<0

(5) Chaplygin gas: p=- A/rho

(6) Phantom: w<-1

(7) Quintom

(8) Chameleon, K-Chameleon

various generalization and mixture……..

3 4 29 3exp crit.

4 19 4 123theor. pl exp

70% (10 ) 10 /

( ) (10 ) 10

ev g cm

M Gev

ρ − −Λ ×

Λ Λ

: : :: : :

QFT, a very successful theory

(1) a very tiny positive cosmological constant ?

Variable cosmological constant? Interaction?

(2) Holographic Energy?

E,S

V,AR

i) Bekenstein Bound: 2S ERπ≤

ii) Holographic Bound: / 4S A G≤

iii) UV/IR Mixture:

(Cohen et al, Hsu, Li….)

(3) Quintessence: a very slowly varying scalar field?

Tracker Potential:

(4) K-essence (Born-Infeld Scalar Field):

( , )p p X φ=

(5) Chaplygin gas ?

/p A ρ=− 61/ 2( )B

aAρ = +

Generalizations:

/0 1p A αρ

α=−< <

( ) / ap A a ρ=−

(6) Phantom (Caldwell, 1999)

1p ww

ρ=< −

2

2

2 ( )2 ( )

s Vws Vφ φφ φ

−=

+

&&

-1<w<0, if s=1

w<-1, if s=-1

(7) Quintom: normal scalar field plus phantom field

W cross the phantom divide, w=-1

(8) Chameleon, K-Chameleon

Hessence ?

2 21 11 2 1 22 2( ) ( ) ( , )L Vφ φ φ φ= ∂ − ∂ −

Acceleration

Deceleration

Distancebetween galaxies

Time (Age of universe)

Beginning

Now (13.7 billion years)

Inflation (acceleration)

Closed, rho<0

Acc.(-1 <w<-1/3)

Super Acc. (w<-1)

? Expand, but w>0

The fate of our universe depends on the nature of dark energy, not only the geometry

Radiation + dust)

(dark energy dominated)

Thanks!