有效场论、全息原理
暴胀宇宙与暗能量
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
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
～
～
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
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]].
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]
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
Equation of Motion of CHDE
Conservation of energy density
EoS for CHDE
Friedman equation
Density with constant
CHDE
Equation of motion for 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
Consistent check from L
At early time of universe
with
Universe with constant
Conformal-age-like Length of CHDE
= -1
= 1/3
EoS of Dark Energy
Epoch:
Inflation
Radiation
Matter
CHDE is a single parameter (d) model like
Today <
More General Analysis
Friedman Equation
Equation of motion for CHDE
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
哈勃年龄（1/H0）
减速
加速
等速
• 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）
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 ηHDE
Conservation of energy density
EoS for ηHDE
Friedman equation
Density with constant
ηHDE
Equation of motion for 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
Expand with respect to
Minimal with respect to
Minimal
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 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%)
Best-Fit Results at 1σ (68.3%) & 2σ (95.4%)
SYSTEMATIC ANALYSIS ON CHDE MODEL
Cosmic evolution of the fractional energy density of CHDE
SYSTEMATIC ANALYSIS ON CHDE MODEL
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 = 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;
Summary
Inflationary Universe
Accelerated Universe
Holographic Principle
Holographic Dark Energy
Cosmological Constant
Understanding Fine-tuning Problem
&
Coincidence Problem
THANKS