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Some Remarks on Dark Energy
Rong-Gen Cai
Institute of Theoretical Physics
Chinese Academy of Sciences
（Nov.6, 2010)
Godfather of Dark Energy: M.S. Turner
Turner, M.S. 1999, The Third Stromlo Symposium: The Galactic Halo, 165, 431
The Concordance Model of the Universe
SNE + CMB + LSS (since 1998):
Inflation⊕Big Bang ⊕Dark Matter ⊕ Dark Energy
(A.Guth, 1981)
4%
23%
⊕ 73%
Challenges:
Inflation model ? Dark matter ? Dark Energy ?
E. Komatsu et al, 2010:
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 geometry
It is dark, but very hot!
Observational evidence from supernovae for an accelerating universe
and a cosmological constant.
By Supernova Search Team (Adam G. Riess et al.). May 1998. 36pp.
Published in Astron.J.116:1009-1038,1998.
e-Print: astro-ph/9805201
Cited 4934 times
Measurements of Omega and Lambda from 42 high redshift supernovae.
By Supernova Cosmology Project (S. Perlmutter et al.). LBNL-41801, LBL-41801,
Dec 1998. 33pp.
The Supernova Cosmology Project.
Published in Astrophys.J.517:565-586,1999.
e-Print: astro-ph/9812133
Cited 5071 times
2010.8.25
SN Ia is not enough!
SN Ia only
Equation of state：w= p /ρ
SN Ia + CMB +BAO
(M. Kowalski et al 2008)
 M. Kowalski et al, 2008
BAO (z=0.2,0.35) +WMAP-5+SN Ia
 E. Komatsu et al, 2010
BAO +WMAP-7 +H_0(=74.2±3.6 km/s/Mpc)
at 68% CL
 E. Komatsu et al, 2010
BAO +WMAP-7 +SNIa +H_0(=74.2±3.6 km/s/Mpc)
at 68% CL
EOS: CPL parameterization：
WMAP-7+…
at 68% CL.
conclusion：
A flat universe with a
tiny cosmological
constant is consistent
with observational
data so far!
Komatsu et al, 1001.4538
Cosmic acceleration dark energy?
Dynamics equations:
p   / 3
(Violate the Strong Energy Condition:
exotic energy component)
What is the nature of the dark energy?
Dark Energy?
Observational Data
R G Cai, 2007
HEP&NP
Theoretical Assumptions
General Relativity
Cosmological Principle
G   8πGT (Λ)
Model I
Model II
Model III
Model I: Modifications of Gravitational Theory
UV: ~ 0.1 mm
1) GR’s test
IR: ~ solar scale
UV: quantum gravity effect
IR: cosmic scale
2) Modify GR
Brane world scenarios
Scalar-tensor theory
……
１) “ 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
gr-qc/0511034:
An alternative explanation of the conflict between 1/R gravity
and solar system tests
C.G. Shao, R.G. Cai, B. Wang and R.K. Su
Phys.Lett. B633 (2006) 164-166
Making a conformal transformation yields a scalar field with potential:
(1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity
Viable f(R) dark energy models:
(Hu and Sawicki, 2007)
(Starobinsky, 2007)
They satisfy f (R=0)=0, the cosmological constant disappears in flat spacetime.
n >0.9 local gravity constraints can be satisfied (S.Tsujikawa,2008)
f(T) model, 2010: Linder, Geng, Yu….
２) Brane World Scenarios:
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: RSII 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

b) DGP Model
SM
3
d
5
x G
(5)
Rm
2
d
4
x  g ( R  Lm )
Then corresponding Friedman equation:
H2 
H
1

(   )
2
rc
6m
rc  m / M
2
3
Two branches:
(+): normal one; phantom if Lambda=\0.
(-): late-time acceleration
c) “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:
“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
Another brane world model with crossing –1:
“Super-acceleration on the Brane by Energy Flow from the Bulk”
R.G. Cai, Y. Gong and B. Wang, JCAP 0603 (2006) 006, hep-th/0511301
Consider the action
Effective dynamic equations:
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
Inhomogeneous Model:
“Inhomogeneous spacetimes as a dark energy model”
D. Garfinkle, gr-qc/0605088, CQG23 (2006) 4811
Recently, many works on LTB model!
Another scenario:
arXiv:0709.0732
PRL99:251101,2007
低密度区
（void)
Model II: Various Dark Energy Models: Acts as Source of E’eq
Dark energy issues:
(1)
(2)
(3) The equation of state crosses –1?
(4) Interaction between dark matter and dark energy?
G   8πGT (Λ)
Model II: Various Dark Energy Models: Acts as Source of E’eq
G   8πGT (Λ)
Some aspects on dark energy：
(1) Equation of state from observational data
(1) Various phenomenological models
(3) How to distinguish those models and new cosmic probers
（1）EOS from observational data
a) Cosmological constant: w = - 1
b) as a constant:
c) expansion by redshift：
d) expansion by scale factor：
parameterization of EOS
-0.11 < 1+w < 0.14
w = const.， phantom ？
( R. Caldwell, astro-ph/9908168, Phys.Lett.B545:23-29,2002)
Note：w <-1: phantom, w >-1: quintessence, w =-1:cosmological const
In terms of bins:
D. Huterer and A. Cooray, astro-ph/040462
S. Qi, F.Y. Wang and T. Lu, 0803.4304
By scale factor：
D. Huterer and G. Starkman, astro-ph/0207517
B. Feng, X. Wang and X. Zhang, astro-ph/0404224
Quintom = quintessence
+ phantom
0903.5141
Om (z) diagnostic:
0904.2832
(Gong, Cai, Chen and Zhu, 0909.0596)
(Gong, Cai, Chen and Zhu, 0909.0596)
0908.3186
0905.1234
DE: constant w and CPL paramertrization
(2) Various dark energy models
G   8πGT (Λ)
(1) Cosmological constant: w=-1
(6) Phantom: w<-1
(2) Holographic energy
(7) Quintom
(3) Quintessence: -1<w<0
(8) Hessence
(4) K-essence: -1 <w<0
(9) Chameleon, K-Chameleon
(5) Chaplygin gas: p=- A/rho
(10) Agegraphic model
(11) Interacting models
……
Dark energy : 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
4
3
~ ( ESUSY ) ~ (10 Gev)
QFT, a very successful theory
This is a problem?
I will come back again.
4
Old Problem on CC:
why
 0
S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)
(1) Supersymmetry; (2) Anthropic princple;
(3) Self-tuning mechanism; (4) Modifying gravity
(5) Quantum cosmology
New Problem on CC:
why
  0 and 
crit
Some remarks:
1) The cosmological constant is undistinguished from the vacuum
expectation value of quantum fields
2) The cosmological constant problem is an issue in quantum gravity
3) The cosmological constant problem is an UV problem
4) The dark energy problem is an IR problem
5) To resolve the dark energy problem: quantum properties of gravity,
UV/IR relation…..
6) Of course, other viewpoints
Application of holography to dark energy：UV/IR Relation
[A.Cohen, D. Kaplan and A. Nelson, PRL 82, 4971 (1999)]
Consider an effective quantum field with UV cutoff Lambda
in a box with size L, its entropy
Black hole mass as an upper bound
UV/IR relation, effective cosmological constant and dark energy
R
What is the IR cutoff L?
A. Cohen et al, (1999): L~Hubble horizon
S. Hsu (2004): L~Hubble horizon
M. Li (2004): L~particle horizon, event horizon
….
Holographic dark energy (Hsu, 2004, Li, 2004) ?
What is the IR Cutoff L for the universe?
(1) Hubble horizon? L=1/H
(2) Particle horizon?
(3) Event horizon?
(4) Other Choices?
While the holographic energy with event horizon works well, however,
Issues here：
 The event horizon is a global concept for manifold;
 It exists only for eternal accelerated universe;
 It is determined by future evolution of the universe
New solution: Causal connection scale:
C.G. Gao et al: arXiv:0712.1394
R.G. Cai et al: arXiv:0812.4504
A new idea on the dark energy: Agegraphic dark energy model
(RGC: arXiv:0707.4049, PLB 657:228-231,2007
(1) General relativity: a classical theory
(2) Quantum mechanics: Heisenberg uncertainty relation
Karolyhazy relation (F. Karolyhazy et al, 1966):
the distance t in Minkowski spacetime cannot be known
to a better accuracy than
The Karolyhazy relation together with the time-energy uncertainty
relation in quantum mechanics leads to a energy density of quantum
fluctuation of spacetime metric (Maziashvili, 2006, 2007)
(N. Sasakura, 1999, Y.J. Ng et al,1994; 2006,2007)
(X. Calmet: hep-th/0701073)
A few features:
(1) energy density exists within a causal patch
(2) obey the holographic entropy bound;
(3) resemble the holographic dark energy
The new proposal is (arXiv:0707.4049)
As the dark energy density in the universe with age T.
A New model for the agegraphic dark energy
(Wei and Cai: arXiv:0708.0884, PLB 660:113-117,2008 )
Dark energy: QCD ghost?
References: F. Urban and A. Zhitnitsky, 0906.2106; 0906.2165;
0906.3546; 0909.2684
N. Ohta, 1010.1339
Other arguments also lead to such a scaling!
Dynamical evolution:
R.G. Cai et al, in preparation
Data fitting:
Furthermore:
Interaction?
The case:
Interaction between dark matter and dark energy?
Interaction and coincidence problem
interaction：
相互作用的分段参数化:
（R.G. Cai and Q.P. Su. 0912.1843)
(3) How to distinguish those models and new cosmic probers
Current probes
New probers？
Revisit the cosmological constant problem
Einstein’s equations (1915):
R
1
 g  R  8 GT
2
The cosmological constant
Two years later (1917),
1
R  g  R  g   8 GT
2
For a static, closed universe model !
(The Greatest Blunder !
?)
Then why the cosmological constant is not good?
1) It is the greatest blunder?
2) The coincidence problem?
3) The worst prediction?
E. Bianchi and C. Rovelli,
1002.3966:
Why all these prejudices against a constant?
1) It is the greatest blunder?
Einstein’s equations (1915):
R
1
 g  R  8 GT
2
The cosmological constant
Two years later (1917),
1
R  g  R  g   8 GT
2
For a static, closed universe model !
(The Greatest Blunder !
?)
G. Gamow, My World Line, 1970
What means by the greatest blunder?
1
R  g  R  g   8 GT
2
2) The coincidence problem?
&
3) The vacuum energy in QFT
about 122 orders of magnitude larger the observed one
Consider:
The effective action:
At one-loop:
i) Planck scale => 122 orders
ii) Tev scale => 55 orders
Do we understand the vacuum energy?
which gives the false result:
The vacuum energy does not gravitate;
The shift of the vacuum energy does gravitate?
Possible answer:
1) The dark energy problem is nothing, but
a cosmological constant problem.
2) The cosmological constant is so far so good!
Thanks!