有效场论、全息原理有效场论、全息原理暴胀宇宙、暗能量暴胀宇宙、暗能量Yue-Liang Wu （吴岳良）吴岳良）State Key Laboratory of Theoretical Physics (SKLTP)Kavli Institute for Theoretical Physics China（KITPC）Institute of Theoretical Physics, Chinese Academy of Sciences2012.05.07Universe 宇宙宇宙 Matter 物质物质3030Dark Energy 暗能量暗能量7070 Dark Matter 暗物质暗物质 85%H (77%) Quark Matter 夸克物质夸克物质15%15%He (23%) 宇宙组份宇宙组份和谐宇宙学模型：和谐宇宙学模型：以以大爆炸宇宙学标准模型大爆炸宇宙学标准模型为基础的为基础的 暴胀暴胀 暗能量暗能量 暗物质暗物质 夸克夸克物质物质暴胀暴胀 现代宇宙学模型现代宇宙学模型Effective Field Theory & Holographic PrincipleEffective Field Theory & Holographic PrincipleAneffectivefieldtheorythatcansaturatetheequationnecessarilyincludesmanystateswithSchwarzschildradiusmuchlargerthantheboxsize.AneffectivequantumfieldtheoryisexpectedtobecapableofdescribingasystematatemperatureT,providedthatT ，solongasT 1/L.ThermalenergyEntropyThecorrespondingSchwarzschildradiusEntropyToavoidthesedifficultiesCohen-Kaplan-Nelson proposeastrongerconstraintontheIRcutoff1/LwhichexcludesallstatesthatliewithintheirSchwarzschildradius.Sincethemaximumenergydensityintheeffectivetheoryis4,theconstraintonLisThermalenergy SchwarzschildradiusLocalquantumfieldtheoryappearsunlikelytobeagoodeffectivelowenergydescriptionofanysystemcontainingablackhole,andshouldprobablynotattempttodescribeparticlestateswhosevolumeissmallerthantheircorrespondingSchwarzschildradius. 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 HoleEffective Theory describes all states of system except those already collapsed to a Black Hole. Vacuum energy density via quantum fluctuation Effective Field Theory & Holographic PrincipleHolographicDarkEnergyHolographic 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 ModelsReview 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 parameterReduced Planck massHolographic Dark Energy Characterized by Conformal-age-like Length (CHDE)Z.P.Huang,YLW,arXiv:1202.2590,Z.P.Huang,YLW,arXiv:1202.3517astro-ph.COConformal-age-likelengthscaleofuniverseMotivated from 4D space-time volume of FRW UniverseHolographic Dark Energy Characterized by Conformal-age-like Length (CHDE)Fractional energy density of CHDEFriedman EquationEquationofMotionofCHDEConservation of energy density Friedman equationEoS for CHDE Equation of motion for CHDEDensity with constant CHDESolutionofEoMforCHDEAt early time of universe Assuming: Dark energy is negligibleEquation of motion for CHDE in a good approximation Solution of EoM for CHDE consistencyInflationary Universe & Conformal-age-like Length of CHDEAt 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 AnalysisEquation of motion for CHDEFriedman Equation Interaction With BackgroundGeneral Equation of motion for CHDEEoS for Dark energy Holographic Dark Energy Characterized by Total Comoving Horizon (HDE)Z.P.Huang,YLW,arXiv:1202.2590,tobepublishedinPRDHolographic Dark Energy Characterized by Total Comoving Horizon (HDE)Total comoving horizon of the universeCharacteristic Length Scale L of Universe from Causality Energy density of holographic dark energyRescaled independent parameter & Fractional DE Density Primordial part of comoving horizon generated by inflationComoving horizon in radiation- & matter-dominated epochgrowsTotal comoving horizon of the universeEnergy density & fractional energy density of dark energybehaves like a cosmological constantFractional energy density of dark energyFraction of dark energy in matter-dominated epochNew agegraphic dark energy (NADE) Avoid DivergenceC.-Y.Sun,R.-H.Yue,Phys.Rev.D83,107302(2011).EquationofMotionofHDEConservation of energy density Friedman equationEoS for HDE Equation of motion for HDEDensity with constant HDEBest-Fit Analysis on HDE ModelsInitial input: Friedman Equation Relevant Cosmological ObservationsUnion2 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,JCAP1201,002(2012)arXiv:1110.0913Type Ia Supernovae (SN Ia) Theoretical Distance modulus Hubble-free luminosity distance Minimal Expand with respect to Minimal with respect toBaryon Acoustic Oscillations (BAO)Volume averaged distanceProperangulardiameterdistanceComoving sound horizonFitting formulaDistanceratioofBAOObservationandanalysisofBAOCosmic Microwave Background (CMB) RadiationAcoustic scale Shift parameterRedshift of the decoupling epochWMAP7 observations and analysis of CMBBest-Fit Results for CHDE Model at 1 (68.3%) and 2 (95.4%)Best-Fit Results at 1 (68.3%) & 2 (95.4%)Best-Fit Results at 1 (68.3%) & 2 (95.4%)SYSTEMATIC ANALYSIS ON CHDE MODELCosmic evolution of the fractional energy density of CHDECosmic evolution of the EoS of CHDESYSTEMATIC ANALYSIS ON CHDE MODELThe decelerating parameterThe statefinder pair j; sSYSTEMATIC ANALYSIS ON CHDE MODELEolution of the decelerating parameterSYSTEMATIC ANALYSIS ON CHDE MODELSYSTEMATIC ANALYSIS ON CHDE MODELThe 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 104On CHDE MODELBest-Fit Results for HDE Model at 1 (68.3%) and 2 (95.4%)Best-Fit Results for HDE Model at 1 (68.3%) and 2 (95.4%) Fractional Energy Density of Dark MatterCosmic evolution of the fractional energy density of HDECosmic evolution of the EoS of HDECosmic evolution of the ratio /d with different d On HDE ModelBehave Like Cosmological ConstantGeneral Class of HDE Modelsn=m=0,ADE;n=0,m=-1,HDE;n=4,m=3,CHDEZ.P. Huang, YLW arXiv:1205.0608 gr-qcTheminimumofbyusingonlytheUnion2SNIadata;forcomparison,Thebest-fitresultsofsomemodelswithn - m = 1 by using only the Union2 SNIa dataThebest-fitbyusingSNIa+BAO+CMBdatasets;forcomparisonThebest-fitresultsat(68.3%)and(95.4%)confidencelevelsbyusingSNIa+BAO+CMBdatasets;Holographic Dark Energy Cosmological Constant Understanding Fine-tuning Problem & Coincidence ProblemInflationary Universe Accelerated UniverseHolographic Principle Summary暗物质和暗能量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二十世纪末物理学和天文学晴朗天空中的“两朵乌云两朵乌云”引力相互作用引力相互作用l与能量有关与能量有关l与物质和运动有关（加速膨胀）与物质和运动有关（加速膨胀）l与真空有关（宇宙常数）与真空有关（宇宙常数）世纪难遇的重大科学问题：世纪难遇的重大科学问题：l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。旦取得突破，将带来一场重大的物理学和天文学革命。l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关，如真空和对称破缺机制，新的基本粒子和物质形态量子引力、物质时空统一理论：必将引发二十一世纪宇宙量子引力、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起源等基本问题有更深的认识新的新的“两朵乌云两朵乌云”“两朵乌云两朵乌云”电磁相互作用电磁相互作用与能量有关与能量有关与物质和运动有关与物质和运动有关与真空有关（与真空有关（以太说以太说 ）1900年，开尔文：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黑体辐射实验和迈克尔逊- -莫雷实验莫雷实验十九世纪末物理学晴朗天空中的十九世纪末物理学晴朗天空中的“两朵乌云两朵乌云”，给物理学，给物理学带来了革命性变革，导致带来了革命性变革，导致“新理论新理论”的发现的发现“量子论量子论”和和“相对论相对论”，极大地推进了人类对物质世界的认识。，极大地推进了人类对物质世界的认识。 热辐射物体能量随发光波长分布：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分别在长波和短波与实验结果不符THANKSTHANKS