Theoretical Aspects of Dark Energy Models

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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
(Violate the Strong Energy Condition

exotic energy component)
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Observation Data
Dark Energy?
Theoretical Assumptions
General Relativity
Cosmo Principle
Model III
Model I
Model II
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Model I Modifications of Gravitational Theory
UV 1 mm IR solar scale
1) GRs test
UV quantum gravity effect IR cosmos
scale Brane World Scenario
2) Modify GR
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Modifying GR in IR

• 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
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More general case hep-th/0410031,
PRD71063513,2005
Consider
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3) Brane World Scenario

• N. Arkani-Hamed et al, 1998
• factorizable product
• 2) L. Randall and R. Sundrum, 1999
• warped product in AdS_5

y
RS1 RS2
3) DGP model, 2000 a brane embedded in a
Minkovski space
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a) A popular model RS scenario
where
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 m0
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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 Primordi
al 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!
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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
cosmologicalconstant
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which indicates the SHCDM with
is indistinguishable from LCDM
model.
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Another scenario
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Beyond the super-horizon modes 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
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Model II Various Dark Energy Models Acts as
Source of Eeq

• Cosmological constant w-1
• (2) Holographic energy
• (3) Quintessence -1ltwlt0
• (4) K-essence -1 ltwlt0
• (5) Chaplygin gas p- A/rho

(6) Phantom wlt-1 (7) Quintom (8) Chameleon,
K-Chameleon various generalization and
mixture..
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(1) a very tiny positive cosmological constant ?
QFT, a very successful theory
Variable cosmological constant? Interaction?
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(2) Holographic Energy?
V,A
E,S
R
i) Bekenstein Bound
ii) Holographic Bound
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)
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(5) Chaplygin gas ?
Generalizations
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(6) Phantom (Caldwell, 1999)
-1ltwlt0, if s1
wlt-1, if s-1
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(7) Quintom normal scalar field plus phantom
field
W cross the phantom divide, w-1
Hessence ?
(8) Chameleon, K-Chameleon
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Super Acc. (wlt-1)
Acc.(-1 ltwlt-1/3)
?
Expand, but wgt0
(dark energy dominated)
Closed, rholt0
Radiation dust)
Inflation (acceleration)
The fate of our universe depends on the nature of
dark energy, not only the geometry
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Thanks!