有效场论、全息原理 暴胀宇宙与暗能量

Effective Field Theory & Holographic Principle 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 Entropy

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 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.

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 Effective Field Theory & Holographic Principle

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 Choosing different characteristic length scale L  Various Holographic Dark Energy Models Review see: M. Li, X. -D. Li, S. Wang, Y. Wang, CTP. 56, (2011) [arXiv: ]. M. Li, Phys. Lett. B 603, 1 (2004) [arXiv:hep-th/ ]. R. -G. Cai, Phys. Lett. B 657, (2007) [arXiv: [hep-th]]. Model parameterReduced Planck mass

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

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

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

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

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

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

More General Analysis Equation of motion for CHDE Friedman Equation

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

Holographic Dark Energy Characterized by Total Comoving Horizon (ηHDE) Z.P. Huang, YLW, arXiv: ,

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

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

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

真实年龄大于哈勃年龄（这一情形在宇宙常数不 为 0 时可能出现） 哈勃年龄 （ 1/H 0 ） 减速加速 等速

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, (2011).

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

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

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

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

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

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

Hubble Constant Hubble constant and analysis

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

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

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

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

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

Eolution of the decelerating parameter 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 = r0 = × 10−4

On CHDE MODEL

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

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

Cosmic evolution of the fractional energy density of ηHDE

Cosmic evolution of the EoS of ηHDE

Cosmic evolution of the ratio η/d with different d

On ηHDE Model Behave Like Cosmological Constant

General Discussion n=m=0, ADE; n=0,m=-1, ηHDE; n=4,m=3, CHDE

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

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;

Holographic Dark Energy Cosmological Constant Understanding Fine-tuning Problem & Coincidence Problem Inflationary Universe Accelerated Universe Holographic Principle Summary

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