Transcript Theoretical Aspects of Dark Energy Models Rong-Gen Cai

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:
H2 
8 G
3

a
4 G

(   3 p)
a
3
p   / 3
(Violate the Strong Energy Condition:
exotic energy component)
Dark Energy?
Observation Data
Theoretical Assumptions
General Relativity
Cosmo Principle
G   8πGT (Λ)
Model I
Model II
Model III
Model I: Modifications of Gravitational Theory
UV: ~ 1 mm
1) GR’s test
IR: ~ solar scale
UV: quantum gravity effect
2) Modify GR
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
R


2( n 1)
Rn
More general case: hep-th/0410031, PRD71:063513,2005
Consider:
3) Brane World Scenario:
X
1) N. Arkani-Hamed et al, 1998

factorizable product
M4 x T n
2) L. Randall and R. Sundrum, 1999
warped product in AdS_5
y
RS1:
cM 4 x S1 / Z 2
RS2:
cM 4 x R
3) DGP model, 2000
a brane embedded in a Minkovski space
a) A popular model: RS scenario
S  161G5  d 5 x  g5 ( R  2 5 )  81G5  d 4 x  g 4 ( K   )
4
8
4

2
H 
(
)  (
)  4
2
3
3
3M 4
3M 5
a
2
where
4
4
2
 4  3 ( 5 
 ) =0
3
M5
3M 5
M4 
3 M 52
(
) M 5 Fine-Tuning
4

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
q :1/ 2  1
cosmological
constant
which indicates the SHCDM with
indistinguishable from LCDM model.
is
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 matter
density we measure locally
Model II: Various Dark Energy Models: Acts as Source of E’eq
G   8πGT (Λ)
(1) Cosmological constant: w=-1
(6) Phantom: w<-1
(2) Holographic energy
(7) Quintom
(3) Quintessence: -1<w<0
(8) Chameleon, K-Chameleon
(4) K-essence: -1 <w<0
(5) Chaplygin gas: p=- A/rho
various generalization and
mixture……..
(1) a very tiny positive cosmological constant ?
 exp
 theor.
crit.  70% (103 ev)4 1029 g / cm3
( M pl )4
(1019 Gev) 4
10123  exp
QFT, a very successful theory
Variable cosmological constant? Interaction?
(2) Holographic Energy?
V,A
R
i) Bekenstein Bound: S  2 ER
ii) Holographic Bound:
S  A / 4G
iii) UV/IR Mixture:
(Cohen et al, Hsu, Li….)
E,S
(3) Quintessence: a very slowly varying scalar field?
Tracker Potential:
(4) K-essence (Born-Infeld Scalar Field):
p  p( X ,  )
(5) Chaplygin gas ?
p  A/ 
  (A )
B 1/ 2
a6
Generalizations:
p  A/ 
0  1

p   A(a) / 
a
(6) Phantom (Caldwell, 1999)
p  w
w  1
-1<w<0, if s=1
s  2V ( )
w 2
s  2V ( )
2
w<-1, if s=-1
(7) Quintom: normal scalar field plus phantom field
L  12 (1 ) 2  12 (2 ) 2  V (1 , 2 )
W cross the phantom divide, w=-1
Hessence ?
(8) Chameleon, K-Chameleon
Super Acc. (w<-1)
Distance
between
galaxies
Acc.(-1 <w<-1/3)
Acceleration
(dark energy dominated)
?
Expand, but w>0
Closed, rho<0
Deceleration
Radiation + dust)
Inflation (acceleration)
Beginning
Now
(13.7 billion
years)
Time (Age of
universe)
The fate of our universe depends on the nature of dark energy, not only the geometr
Thanks!