有效场论、全息原理 暴胀宇宙与暗能量
有效场论、全息原理 暴胀宇宙与暗能量
Effective Field Theory Holographic Principle Entropy SNL3A3 3A3≤SBH=D2M 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 sA, so long as T >>1/L Thermal energy MLT Entropy S~L732m=n⑦~(M/L The corresponding schwarzschild radius LSN L(LMP)2/>L
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
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 M4, the constraint on L is L3A4≤LM Thermal energy M~L374≈1L3A4 La 2gm Schwarzschild radius r Ls L
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
Effective Field Theory Holographic Principle Holographic Principle: (Cohen-Kaplan-Nelson, PRL1999 In Effective Field Theory, UV Cut-off u is related to the IR Cut-off L due to the limit set by the formation of a black hole 4 LA LM LIV Effective Theory describes all states of system except those already collapsed to a Black Hole Vacuum energy density via quantum fluctuation 2 vac 4 N MAL A uV
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 Pde=3 2M2L-2 L Characteristic length scale of universe Model parameter MP 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]l
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, 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]
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 dt dta(r) a4(r)≡ dna() +(t √0 al ar+(1) Motivated from 4D space-time volume of FRW Universe g a(t)· dra(t) 0 0 Fractional energy density of CHDe Friedman Equation pde d- e 3M2H2 H2L2 3M#H=Pm pde
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 CHe Conservation of energy density Friedman equation p+3H(1+w)=0田9+Qn=1 Eos for Che Density with constant Wm 82V9 3 3d a IOm= C1a-3(1+Wm) CHDE 1+3m)(1 Ha aa rd V3MF o H'a vdHa Equation of motion for CHDE dede Q2 (1-92)3(1+wm)+8 a
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 cede At early time of universe a≤1 Assuming Dark energy is negligible de Equation of motion for CHDE in a good approximation d e 3(1+wm)+8、2√gde de Solution of eom for CHDe consIstency Qde a -(3+Wm)2d2a2 Qde <1 a<1
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
nflationary Universe Conformal-age-like Length of CHDE Consistent check from L- I c 0 0 ha At early time of universe a< 1with Q≈1 Universe with constant 3(1+wm Conformal-age-like Length of CHDE 2 L a/ 3(3+Wm)Ha Haia 1)2=d( a)<1-L Odee(3+Wm)2d2a 3(3+Wm)ha 4 Wm=-1 m=1/3 L-3hal n de 9da2L-shalode e 25d-a2
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