Download - Some Remarks on Dark Energy
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Some Remarks on Dark Energy
Rong-Gen CaiInstitute of Theoretical PhysicsChinese Academy of Sciences ( Huangshan, April 9, 2011)
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Godfather of Dark Energy: M.S. Turner
Turner, M.S. 1999, The Third Stromlo Symposium: The Galactic Halo, 165, 431
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Inflation Big Bang ⊕ ⊕Dark Matter ⊕ Dark Energy (A.Guth, 1981) 4% 23% 73% ⊕
Challenges: Inflation model ? Dark matter ? Dark Energy ?
SNE + CMB + LSS (since 1998):
E. Komatsu et al, 2010:
The Concordance Model of the Universe
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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
It is dark, but very hot!
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Papers entitled “ dark energy”: 2154Papers entitled “ cosmological constant”: 1735
Papers in SLAC databases
0
50
100
150
200
250
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1999 2001 2003 2005 2007 2009
4000in total
exponential growth stabilized
2009.12.09
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SN Ia is not enough!
(M. Kowalski et al 2008)
SN Ia only SN Ia + CMB +BAO
Equation of state: w= p /ρ
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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)
E. Komatsu et al, 2010 BAO +WMAP-7 +SNIa +H_0(=74.2±3.6 km/s/Mpc)
at 68% CL
at 68% CL
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Cosmic acceleration dark energy?
Dynamics equations:
/ 3p (Violate the Strong Energy Condition: exotic energy component)
What is the nature of the dark energy?
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Dark Energy?Observational Data
Theoretical Assumptions
General Relativity Cosmological Principle
G 8πGT (Λ)
Model I Model II Model III
R G Cai, 2007 HEP&NP
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Model I: Modifications of Gravitational Theory
1) GR’s test
UV: ~ 0.1 mm
IR: ~ solar scale
2) Modify GR
UV: quantum gravity effect
IR: cosmic scale
Brane world scenarios
Scalar-tensor theory……
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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 testsC.G. Shao, R.G. Cai, B. Wang and R.K. SuPhys.Lett. B633 (2006) 164-166
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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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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….
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2 ) Brane World Scenarios:
y
X 1) 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 Z
cM
3) DGP model, 2000 a brane embedded in a Minkovski space
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a) A popular model: RSII scenario
5 5
5 41 15 5 416 8( 2 ) ( )G GS d x g R d x g K
2 242 3 44 5
8 4( ) ( )
3 3 3H
M M a
where2
4 53 35 5
25
4 5
4 4( )
3
3( )
4
M M
MM M
= 0
Fine-Tuning
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b) DGP Model
3 5 (5) 2 4 ( )mS M d x G R m d x g R L
Then corresponding Friedman equation:
22
1( )
6c
HH
r m 2 3/cr m M
Two branches: (+): normal one; phantom if Lambda=\0. (-): late-time acceleration
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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:
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In general they have two branches:
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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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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
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Effective dynamic equations:
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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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Inhomogeneous Model:
“Inhomogeneous spacetimes as a dark energy model”
D. Garfinkle, gr-qc/0605088, CQG23 (2006) 4811
Recently, many works on LTB model!
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Another scenario:
arXiv:0709.0732PRL99:251101,2007 低密度区
( void)
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(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
Dark energy issues:
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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
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( 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
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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
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D. Huterer and A. Cooray, astro-ph/040462
In terms of bins:
S. Qi, F.Y. Wang and T. Lu, 0803.4304
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By scale factor :
D. Huterer and G. Starkman, astro-ph/0207517
B. Feng, X. Wang and X. Zhang, astro-ph/0404224
Quintom = quintessence + phantom
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0903.5141
Om (z) diagnostic:
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0904.2832
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(Gong, Cai, Chen and Zhu, 0909.0596)
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(Gong, Cai, Chen and Zhu, 0909.0596)
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0908.3186
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0905.1234
DE: constant w and CPL paramertrization
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Probing the dynamical behavior of dark energyR.G. Cai et al. 1001.2207, JCAP 2010
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G 8πGT (Λ)
(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) Hessence
(9) Chameleon, K-Chameleon
(10) Agegraphic model
(11) Interacting models ……
(2) Various dark energy models
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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
QFT, a very successful theory
Dark energy : a very tiny positive cosmological constant ?
4 3 4~ ( ) ~ (10 )SUSYE Gev
This is a problem? I will come back again.
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Old Problem on CC:
why S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)
0
(1)Supersymmetry; (2) Anthropic princple;(3) Self-tuning mechanism; (4) Modifying gravity(5) Quantum cosmology
New Problem on CC:
why crit0 and
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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
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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
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Holographic principle?
E,S
V,AR
i) Bekenstein Bound: 2S ER
ii) Holographic Bound: / 4S A G
iii) UV/IR Mixture:
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R
UV/IR relation, effective cosmological constant and dark energy
A. Cohen et al, (1999): L~Hubble horizon S. Hsu (2004): L~Hubble horizon M. Li (2004): L~particle horizon, event horizon….
What is the IR cutoff L?
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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?
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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
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A new idea on the dark energy: Agegraphic dark energy model
(RGC: arXiv:0707.4049, PLB 657:228-231,2007
Karolyhazy relation (F. Karolyhazy et al, 1966):
(1) General relativity: a classical theory(2) Quantum mechanics: Heisenberg uncertainty relation
the distance t in Minkowski spacetime cannot be known to a better accuracy than
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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)
A few features: (1) energy density exists within a causal patch (2) obey the holographic entropy bound; (3) resemble the holographic dark energy
(X. Calmet: hep-th/0701073)
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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 )
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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!
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Dynamical evolution: R.G. Cai et al, 1011.3212
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Data fitting:
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Furthermore:
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Interaction?
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The case:
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Interaction between dark matter and dark energy?
Interaction and coincidence problem
interaction :
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相互作用的分段参数化 :
( R.G. Cai and Q.P. Su. 0912.1843, PRD 2010)
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(3) How to distinguish those models and new cosmic probers
Current probes
New probes?
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Einstein’s equations (1915):
18
2R g R g GT
18
2R g R GT
Two years later (1917),The cosmological constant
For a static, closed universe model !
(The Greatest Blunder ! ?)
Revisit the cosmological constant problem
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EOS: CPL parameterization:
Komatsu et al, 1001.4538
WMAP-7+…
at 68% CL.
conclusion:A flat universe with atiny cosmologicalconstant is consistent with observational data so far!
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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?
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Einstein’s equations (1915):
18
2R g R g GT
18
2R g R GT
Two years later (1917),The cosmological constant
For a static, closed universe model !
(The Greatest Blunder ! ?)
G. Gamow, My World Line, 1970
1) It is the greatest blunder?
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What means by the greatest blunder?
18
2R g R g GT
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2) The coincidence problem?
&
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3) The vacuum energy in QFT
about 122 orders of magnitude larger the observed one
Consider:
The effective action:
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At one-loop:
i) Planck scale => 122 ordersii) Tev scale => 55 orders
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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?
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1) The dark energy problem is nothing, but a cosmological constant problem.
2) The cosmological constant is so far so good!
Possible answer:
![Page 74: Some Remarks on Dark Energy](https://reader035.vdocuments.mx/reader035/viewer/2022062309/568151f4550346895dc02daf/html5/thumbnails/74.jpg)
Thanks!