Some Remarks on Dark Energy Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences （Huangshan, April 9, 2011)
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:
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
Papers in SLAC databases 4000 in total Papers entitled “ dark energy”: 2154 Papers entitled “ cosmological constant”: 1735 2009.12.09 exponential growth stabilized
SN Ia is not enough! SN Ia only SN Ia + CMB +BAO Equation of state：w= p /ρ (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) • E. Komatsu et al, 2010 BAO +WMAP-7 +SNIa +H_0(=74.2±3.6 km/s/Mpc) at 68% CL at 68% CL
Cosmic acceleration dark energy? Dynamics equations: (Violate the Strong Energy Condition:exotic energy component) What is the nature of the dark energy?
Dark Energy? R G Cai, 2007 HEP&NP Observational Data Theoretical Assumptions General Relativity Cosmological Principle Model III ModelI Model II
Model I: Modifications of Gravitational Theory UV: ~ 0.1 mm IR: ~ solar scale 1) GR’s test UV: quantum gravity effect IR: cosmic scale Brane world scenarios Scalar-tensor theory …… 2) Modify GR
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 andSawicki, 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: • 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
a) A popular model: RSII scenario where = 0 Fine-Tuning
b) DGP Model Then corresponding Friedman equation: 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:
“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
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) • The equation of state crosses –1? • Interaction between dark matter and dark energy?
Model II: Various Dark Energy Models: Acts as Source of E’eq Some aspects on dark energy： • Equation of state from observational data • Various phenomenological models • 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) -0.11 < 1+w < 0.14 expansion by scale factor： parameterization of EOS
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:
0905.1234 DE: constant w and CPL paramertrization
Probing the dynamical behavior of dark energy R.G. Cai et al. 1001.2207, JCAP 2010
(2) Various dark energy models • 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 ……
Dark energy : a very tiny positive cosmological constant ? QFT, a very successful theory This is a problem? I will come back again.
Old Problem on CC: why S. Weinberg, Rev. Mod. Phys. 61, 1 (1989) • Supersymmetry; (2) Anthropic princple; • (3) Self-tuning mechanism; (4) Modifying gravity • (5) Quantum cosmology New Problem on CC: why
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
Holographic principle? V,A E,S R i) Bekenstein Bound: ii) Holographic Bound: iii) UV/IR Mixture:
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? • Hubble horizon? L=1/H • Particle horizon? • 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