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Some Remarks on Dark Energy

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.

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Some Remarks on Dark Energy

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  1. Some Remarks on Dark Energy Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences （Nov.6, 2010)

  2. Godfather of Dark Energy: M.S. Turner Turner, M.S. 1999, The Third Stromlo Symposium: The Galactic Halo, 165, 431

  3. 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:

  4. Distance between galaxies Acceleration Deceleration Now (13.7 billionyears) Beginning Time (Age of universe) SuperAcc. (w<-1) Acc.(-1 <w<-1/3) ? Expand, but w>0 (dark energy dominated) Closed, rho<0 Radiation + dust) Inflation (acceleration) The fate of our universe depends on the nature of dark energy, not only the geometry

  5. 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

  6. SN Ia is not enough! SN Ia only SN Ia + CMB +BAO Equation of state：w= p /ρ (M. Kowalski et al 2008)

  7. 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

  8. 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

  9. Cosmic acceleration dark energy? Dynamics equations: (Violate the Strong Energy Condition:exotic energy component) What is the nature of the dark energy?

  10. Dark Energy? R G Cai, 2007 HEP&NP Observational Data Theoretical Assumptions General Relativity Cosmological Principle Model III ModelI Model II

  11. 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

  12. 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

  13. Making a conformal transformation yields a scalar field with potential: (1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity

  14. 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….

  15. 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

  16. a) A popular model: RSII scenario where = 0 Fine-Tuning

  17. b) DGP Model Then corresponding Friedman equation: Two branches: (+): normal one; phantom if Lambda=\0. (-): late-time acceleration

  18. 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:

  19. In general they have two branches:

  20. “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

  21. 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

  22. Effective dynamic equations:

  23. 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

  24. Inhomogeneous Model: “Inhomogeneous spacetimes as a dark energy model” D. Garfinkle, gr-qc/0605088, CQG23 (2006) 4811 Recently, many works on LTB model!

  25. Another scenario: arXiv:0709.0732 PRL99:251101,2007 低密度区 （void)

  26. 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?

  27. 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

  28. （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

  29. 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

  30. In terms of bins: D. Huterer and A. Cooray, astro-ph/040462 S. Qi, F.Y. Wang and T. Lu, 0803.4304

  31. By scale factor： D. Huterer and G. Starkman, astro-ph/0207517 B. Feng, X. Wang and X. Zhang, astro-ph/0404224 Quintom = quintessence + phantom

  32. 0903.5141 Om (z) diagnostic:

  33. 0904.2832

  34. (Gong, Cai, Chen and Zhu, 0909.0596)

  35. (Gong, Cai, Chen and Zhu, 0909.0596)

  36. 0908.3186

  37. 0905.1234 DE: constant w and CPL paramertrization

  38. (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 ……

  39. Dark energy : a very tiny positive cosmological constant ? QFT, a very successful theory This is a problem? I will come back again.

  40. 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

  41. 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

  42. 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

  43. 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 ….

  44. 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?

  45. 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

  46. A new idea on the dark energy: Agegraphic darkenergy model (RGC: arXiv:0707.4049, PLB 657:228-231,2007 • General relativity: a classical theory • 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

  47. 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

  48. 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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