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![Page 1: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/1.jpg)
Theoretical Aspects of Dark Energy Models
Rong-Gen Cai
Institute of Theoretical Physics
Chinese Academy of Sciences
CCAST, July 4, 2005
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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)
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Dark Energy? Observation Data
Theoretical Assumptions
General Relativity Cosmo Principle
G 8∂GT (Ë )μν μν=
Model I Model II Model III
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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
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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.
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Consider a ghost field with a wrong-sign kinetic term:
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Suppose the scalar field has a constant velocity:
The low-energy effective action for the fluctuation has an usual form:
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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
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Making a conformal transformation yields a scalar field with potential:
(1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity
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General case:
4 2( 1)n
nR Rμ μ +
→
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More general case: hep-th/0410031, PRD71:063513,2005
Consider:
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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
![Page 13: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/13.jpg)
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
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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:
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In general they have two branches:
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Current value of the effective equation of state of “dark energy”
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The acceleration can be a transient phenomenon: Brane 2
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However, w crosses –1, the phantom divide? D. Huterer and A. Cooray, astro-ph/040462; Phys.Rev. D71 (2005) 023506
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“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
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The equations of motion:
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The effective equation of state of “dark energy”:
Where the Gauss-Bonnet term in the bulk and bulk mass play a curial role.
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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
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Inflation produces super-horizon perturbations!
![Page 26: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/26.jpg)
Consider the presence of cosmic perturbations,
Split the gravitational potential to two parts
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A local observer within the Hubble volume will see
:1/ 2 1q → −
cosmologicalconstant
![Page 28: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/28.jpg)
which indicates the SHCDM with is indistinguishable from LCDM model.
![Page 29: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/29.jpg)
Another scenario:
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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
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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……..
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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?
![Page 34: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/34.jpg)
(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….)
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(3) Quintessence: a very slowly varying scalar field?
Tracker Potential:
(4) K-essence (Born-Infeld Scalar Field):
( , )p p X φ=
![Page 36: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/36.jpg)
(5) Chaplygin gas ?
/p A ρ=− 61/ 2( )B
aAρ = +
Generalizations:
/0 1p A αρ
α=−< <
( ) / ap A a ρ=−
![Page 37: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/37.jpg)
(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
![Page 38: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/38.jpg)
(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= ∂ − ∂ −
![Page 39: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/39.jpg)
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)
![Page 40: Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1ad17f8b9ab0599718a2/html5/thumbnails/40.jpg)
Thanks!