2. Some Remarks on Dark Energy Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences （ Huangshan, April 9, 2011)

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

4. 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

5. 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/9805201Adam G. Riess et al. Cited 4934 times4934 times Measurements of Omega and Lambda from 42 high redshift supernovae. By Supernova Cosmology Project (S. Perlmutter et al.). LBNL-41801, LBL-41801,S. Perlmutter et al. Dec 1998. 33pp. The Supernova Cosmology Project. Published in Astrophys.J.517:565-586,1999. e-Print: astro-ph/9812133 Cited 5071 times 5071 times 2010.8.25 It is dark, but very hot!

6. Papers entitled “ dark energy”: 2154 Papers entitled “ cosmological constant”: 1735 Papers in SLAC databases 4000 in total exponential growth stabilized 2009.12.09

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

8.  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

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? Observational Data Theoretical Assumptions General RelativityCosmological Principle Model IModel II Model III R G Cai, 2007 HEP&NP

11. 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 ……

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 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….

15. ２ ) Brane World Scenarios: y 1) N. Arkani-Hamed et al, 1998 factorizable product 2) L. Randall and R. Sundrum, 1999 warped product in AdS_5 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. (1) (2) (3) The equation of state crosses –1? (4) Interaction between dark matter and dark energy? Model II: Various Dark Energy Models: Acts as Source of E’eq Dark energy issues:

27. Model II: Various Dark Energy Models: Acts as Source of E’eq 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

28. （ 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

29. w = const. ， phantom ？ ( R. Caldwell, astro-ph/9908168, Phys.Lett.B545:23-29,2002) Note ： w -1: quintessence, w =-1:cosmological const

30. D. Huterer and A. Cooray, astro-ph/040462 In terms of bins: 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:

34. 0904.2832

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

38. 0908.3186

39. 0905.1234 DE: constant w and CPL paramertrization

40. Probing the dynamical behavior of dark energy R.G. Cai et al. 1001.2207, JCAP 2010

43. (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

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

45. Old Problem on CC: why 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

46. 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

47. 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

48. Holographic principle? E,S V,A R i) Bekenstein Bound: ii) Holographic Bound: iii) UV/IR Mixture:

49. 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?

50. 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?

51. 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

52. 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

53. 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)

54. 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 )

55. 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!

56. Dynamical evolution: R.G. Cai et al, 1011.3212

57. Data fitting:

59. Furthermore:

60. Interaction?

61. The case:

62. Interaction between dark matter and dark energy? Interaction and coincidence problem interaction ：

63. 相互作用的分段参数化 : （ R.G. Cai and Q.P. Su. 0912.1843, PRD 2010)

64. (3) How to distinguish those models and new cosmic probers Current probes New probes ？

65. Einstein’s equations (1915): Two years later (1917), The cosmological constant For a static, closed universe model ! (The Greatest Blunder ! ?) Revisit the cosmological constant problem

66. EOS: CPL parameterization ： Komatsu et al, 1001.4538 WMAP-7+… at 68% CL. conclusion ： A flat universe with a tiny cosmological constant is consistent with observational data so far!

67. 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?

68. Einstein’s equations (1915): 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?

69. What means by the greatest blunder?

70. 2) The coincidence problem? &

71. 3) The vacuum energy in QFT about 122 orders of magnitude larger the observed one Consider: The effective action:

72. At one-loop: i)Planck scale => 122 orders ii)Tev scale => 55 orders

73. 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?

74. 1) The dark energy problem is nothing, but a cosmological constant problem. 2) The cosmological constant is so far so good! Possible answer:

75. Thanks!