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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 EnergyHolographic 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, 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]].
Model parameter Reduced Planck mass
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]
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 CHDE Friedman Equation
Equation of Motion of CHDEConservation 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:1202.2590,
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/H0)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, 107302 (2011) .
Equation of Motion of ηHDEConservation 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 distance Proper 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 ConstantHubble 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%)
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
SYSTEMATIC ANALYSIS ON CHDE MODEL
The statefinder parameter j− s contour evolves in redshift inteval z [−0.2; 15]∈ (The arrow indicatesthe evolution from high redshift to low redshift); Model parameters take the best-fit values, i.e.d = 0.235 r0 = 3.076 × 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
THANKSTHANKS