有效场论、全息原理 暴胀宇宙、暗能量

1. 有效场论、全息原理 暴胀宇宙、暗能量 Yue-Liang Wu （吴岳良） State Key Laboratory of Theoretical Physics (SKLTP) Kavli Institute for Theoretical Physics China（KITPC） Institute of Theoretical Physics, Chinese Academy of Sciences 2012.05.07

2. 现代宇宙学模型 宇宙组份 暴胀 Dark Energy 暗能量～70％ Dark Matter暗物质85% Universe 宇宙 H (77%) Matter物质～30％ Quark Matter夸克物质15% He (23%) 和谐宇宙学模型：以大爆炸宇宙学标准模型为基础的 暴胀暗能量暗物质夸克物质

3. Effective Field Theory & Holographic Principle

4. Effective Field Theory & Holographic Principle Entropy An effective field theory that can saturate the equation necessarily includes many states with Schwarzschild radius much larger than the box size. An effective quantum field theory is expected to be capable of describing a system at a temperature T , provided that T ≤ Λ，so long as T ≫ 1/L. Thermal energy Entropy The corresponding Schwarzschild radius

5. Local quantum field theory appears unlikely to be a good effective low energy description of any system containing a black hole, and should probably not attempt to describe particle states whose volume is smaller than their corresponding Schwarzschild radius. To avoid these difficulties Cohen-Kaplan-Nelson propose a stronger constraint on the IR cutoff 1/L which excludes all states that lie within their Schwarzschild radius. Since the maximum energy density in the effective theory is Λ^4, the constraint on L is Thermal energy ～ ～ Schwarzschild radius

6. Effective Field Theory & Holographic Principle Holographic Principle: (Cohen-Kaplan-Nelson, PRL1999) In Effective Field Theory, UV Cut-off is related to the IR Cut-off due to the limit set by the formation of a Black Hole Effective Theory describes all states of system except those already collapsed to a Black Hole. Vacuum energy density via quantum fluctuation

7. Holographic Dark Energy Holographic Dark Energy Model: Dark energy density is given by the vacuum energy density caused via quantum fluctuation Characteristic length scale of universe Model parameter Reduced Planck mass Choosing different characteristic length scale L  Various Holographic Dark Energy Models Review see: M. Li, X. -D. Li, S. Wang, Y. Wang, CTP. 56, 525-604 (2011) [arXiv:1103.5870]. M. Li, Phys. Lett. B 603, 1 (2004) [arXiv:hep-th/0403127]. R. -G. Cai, Phys. Lett. B 657, 228-231 (2007) [arXiv:0707.4049 [hep-th]].

8. Holographic Dark Energy Characterized by Conformal-age-like Length (CHDE) Z.P. Huang, YLW, arXiv:1202.2590, Z.P. Huang, YLW, arXiv:1202.3517 [astro-ph.CO]

9. Holographic Dark Energy Characterized by Conformal-age-like Length (CHDE) Conformal-age-like length scale of universe Motivated from 4D space-time volume of FRW Universe Fractional energy density of CHDE Friedman Equation

10. Equation of Motion of CHDE Conservation of energy density Friedman equation EoS for CHDE Density with constant CHDE Equation of motion for CHDE

11. Solution of EoM for CHDE At early time of universe Assuming: Dark energy is negligible Equation of motion for CHDE in a good approximation Solution of EoM for CHDE consistency

12. Inflationary Universe & Conformal-age-like Length of CHDE Consistent check from L At early time of universe with Universe with constant Conformal-age-like Length of CHDE = -1 = 1/3

13. EoS of Dark Energy Epoch: Inflation Radiation Matter Today < CHDE is a single parameter (d) model like

14. More General Analysis Friedman Equation Equation of motion for CHDE

15. Interaction With Background General Equation of motion for CHDE EoS for Dark energy

16. Holographic Dark Energy Characterized by Total Comoving Horizon (ηHDE) Z.P. Huang, YLW, arXiv:1202.2590, to be published in PRD

17. Holographic Dark Energy Characterized by Total Comoving Horizon (ηHDE) Total comoving horizon of the universe Characteristic Length Scale L of Universe from Causality Energy density of holographic dark energy Rescaled independent parameter & Fractional DE Density

18. Primordial part of comoving horizon generated by inflation Comoving horizon in radiation- & matter-dominated epoch grows

19. Total comoving horizon of the universe Energy density & fractional energy density of dark energy behaves like a cosmological constant

20. Fractional energy density of dark energy Fraction of dark energy in matter-dominated epoch New agegraphic dark energy (NADE) Avoid Divergence C. -Y. Sun, R. -H. Yue, Phys. Rev. D 83, 107302 (2011) .

21. Equation of Motion of ηHDE Conservation of energy density Friedman equation EoS for ηHDE Density with constant ηHDE Equation of motion for ηHDE

22. Best-Fit Analysis on HDE Models Initial input: Friedman Equation

23. Relevant Cosmological Observations • Union2 compilation of 557 supernova Ia (SNIa) data, • Baryon acoustic oscillation (BAO) results from the Sloan Digital Sky Survey data release 7 (SSDS DR7) , • Cosmic microwave background radiation (CMB) data from 7-yr Wilkinson Microwave Anisotropy Probe (WMAP7) • Hubble constant H measurement from the Wide Field Camera 3 on the Hubble SpaceTelescope (HSTWFC3) Likelihood function and Minimal C.Q.Geng, C.C.Lee , E.N.Saridakis, JCAP 1201, 002 (2012) [arXiv:1110.0913 ]

24. Type Ia Supernovae (SN Ia) Theoretical Distance modulus Hubble-free luminosity distance Minimal Expand with respect to Minimal with respect to

25. Baryon Acoustic Oscillations (BAO) Volume averaged distance Proper angular diameter distance Comoving sound horizon Fitting formula Distance ratio of BAO Observation and analysis of BAO

26. Cosmic Microwave Background (CMB) Radiation Acoustic scale Shift parameter Redshift of the decoupling epoch WMAP7 observations and analysis of CMB

27. Best-Fit Results for CHDE Model at 1σ (68.3%) and 2σ (95.4%)

28. Best-Fit Results at 1σ (68.3%) & 2σ (95.4%)

29. Best-Fit Results at 1σ (68.3%) & 2σ (95.4%)

30. SYSTEMATIC ANALYSIS ON CHDE MODEL Cosmic evolution of the fractional energy density of CHDE

31. SYSTEMATIC ANALYSIS ON CHDE MODEL Cosmic evolution of the EoS of CHDE

32. SYSTEMATIC ANALYSIS ON CHDE MODEL The decelerating parameter The statefinder pair { j; s}

33. SYSTEMATIC ANALYSIS ON CHDE MODEL Eolution of the decelerating parameter

34. SYSTEMATIC ANALYSIS ON CHDE MODEL The statefinder parameter j− s contour evolves in redshift inteval z ∈ [−0.2; 15] (The arrow indicates the evolution from high redshift to low redshift); Model parameters take the best-fit values, i.e. d = 0.235 r0 = 3.076 × 10−4

35. On CHDE MODEL

36. Best-Fit Results for ηHDE Model at 1σ (68.3%) and 2σ (95.4%)

37. Best-Fit Results for ηHDE Model at 1σ (68.3%) and 2σ (95.4%) Fractional Energy Density of Dark Matter

38. Cosmic evolution of the fractional energy density of ηHDE

39. Cosmic evolution of the EoS of ηHDE

40. Cosmic evolution of the ratio η/dwith different d

41. On ηHDE Model Behave Like Cosmological Constant

42. General Class of HDE Models Z.P. Huang, YLW arXiv:1205.0608 [gr-qc] n=m=0, ADE; n=0,m=-1, ηHDE; n=4,m=3, CHDE

43. The minimum of by using only the Union2 SNIa data; for comparison, The best-fit results of some models with n -m = 1 by using only the Union2 SNIa data

44. The best-fit by using SNIa+BAO+CMB data sets; for comparison The best-fit results at (68.3%) and (95.4%) confidence levels by using SNIa+BAO+CMB data sets;

45. Summary Inflationary Universe Accelerated Universe Holographic Principle Holographic Dark EnergyCosmological Constant Understanding Fine-tuning Problem & Coincidence Problem

46. 新的“两朵乌云” 暗物质和暗能量 二十世纪末物理学和天文学晴朗天空中的“两朵乌云” 世纪难遇的重大科学问题： • 理解暗物质和暗能量问题同样需要发展和建立新的理论，一旦取得突破，将带来一场重大的物理学和天文学革命。 • 与粒子物理和量子场论所涉及到的最基本的关键问题密切相关，如真空和对称破缺机制，新的基本粒子和物质形态 引力相互作用 • 与能量有关 • 与物质和运动有关（加速膨胀） • 与真空有关（宇宙常数） 量子引力、物质时空统一理论：必将引发二十一世纪宇宙 起源等基本问题有更深的认识

47. “两朵乌云” 1900年，开尔文：“ There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.”，“Two small, puzzling clouds remained on the horizon”——黑体辐射实验和迈克尔逊-莫雷实验 电磁相互作用 • 与能量有关 • 与物质和运动有关 • 与真空有关（以太说 ） 热辐射物体能量随发光波长分布：维恩公式和瑞利一金斯公式 分别在长波和短波与实验结果不符 十九世纪末物理学晴朗天空中的“两朵乌云”，给物理学带来了革命性变革，导致“新理论”的发现——“量子论”和“相对论”，极大地推进了人类对物质世界的认识。

48. THANKS 谢谢！