暗能量、残余引力波、暗能量、残余引力波、CMB极化极化Darkenergy,relicGWandCMBpolarization 张杨(YangZhang)中国科学技术大学(USTC)天体物理中心(CFA)7/23/20241OutlineOfTopics一、一、 Cosmic Dark Energy二、二、 Relic Gravitational Waves三、三、 CMB Polarizations by RGW7/23/20242一、一、 Cosmic Dark Energy- the effective YM condensate model7/23/20243Observational Evidence for Accelerating ExpansionSNIa型超新星Riess(1998)Permutter(1999)Tonry(2003),z=0.31.3,8newKnop(2003),z=0.36-0.86,11newCMBanisotropies(WMAP)Largescalestructureetc.7/23/20244Models for Dark Energy:1. Cosmologicalconstant:2.Effectivegravity:L=R+bRlnR+3.scalarfield：quintessence,k-essence,etc4. Bag-Model(T.D.Lee)=const.5. EffectiveYang-Millscondensate7/23/20245Coincidence Problem：7/23/20246strategy:constructatrackingsolution,thepresentstateisinsensitivetotheinitialconditions.7/23/20247 EffectiveYang-Millscondensate:Idea:WhatiftheUniverseisfilledwithquantumeffectiveYMcondensateasthegroundstate?TheuniverseisquitesimilartotheQCDvacuuminhadrons,towhichthequantumeffectiveYang-Millscondensatecontributes.7/23/20248Recall:MITBagConstant:Idea:Quarksinsidehadronsfeelavacuumwith=B, p= -B, whereBisMITBagconstant.QCDvacuuminhadronscanbephenomenologicallydescribedbytheB,towhichthegluoncondensatecontributes.7/23/202497/23/202410Interestingfeatures:quantumeffective1-loopcontribution;gaugeinvariance;Lorentzinvariance;correcttraceanomaly;7/23/2024117/23/202412Observethat:theeffectiveYMcondensatebehavesasathighenergies,pyy/3,radiationatlowenergies,py-y,darkenergyThiswillleadtothescalingbehavior,andthetracksolution.7/23/202413Friedmannequation:7/23/2024147/23/202415Non-interaction:7/23/202416Interactionwithmatter:7/23/202417Themodel1:i.e.theYMcondensatedecaysintomatterattherate.7/23/2024187/23/2024197/23/2024207/23/202421Remark:AtrackersolutionexistsforawiderangeoftheinitialYMenergydensity;Thepresentstate0.73,m0.27isrealizednaturallyasaresultofevolution;7/23/202422wy=y/py goesfrom1/3crossesover-1,andsettlesdowntow-1;Otherchoicesof/H also yield similar evolution behavior; m levels off; 7/23/202423Theasymptoticbehaviorofthetrackersolutionwithy0.73,m0.27,astItisafixedpoint,anditisstable.7/23/202424Phasegraphfortrajectories:7/23/202425Themodel2:i.e.thematterdecaysintotheYMcondensateatarate.7/23/2024267/23/2024277/23/2024287/23/202429Remark:similartothemodel1wy=y/py also goesfrom1/3,andapproachesto-1,butdoesnotgotow-1.8 is ruled out by LIGO; 7/23/202462Nucleosynthesis bound puts =-1.9 in danger;The model =-2.0 is still robust.Reheating enhances the high frequency amplitude, which may be detectable.7/23/202463三、三、CMB Polarizations induced by RGW7/23/202464MagnetictypeofCMBpolarizationcanonlybeproducedbyGW.-ThisgivesawaytodetectGWonlargescales.WehaveobtainedtheanalyticexpressionsfortheCMBpolarizationspectra.7/23/202465Sachs-Wolfeterm:7/23/2024667/23/202467InPolnarevsmethodtheBolzmannsequationreducesto:7/23/2024687/23/202469ThepolarizationspectraofCMB:7/23/202470Asasource,GWisgivenby:7/23/2024717/23/2024727/23/202473PolarizationsaregeneratedviaThompsonScatteringduringthedecoupling.Itisdescribedbytheopticaldepth,ormoreconveniently,bythevisibilityfunctionV(t).7/23/202474ThevisibilityfunctionisusallymodeledbyaGaussianfunction,butwemodelitbytwopiecesofhalf-Gaussiancurves:7/23/2024757/23/202476V(t)dependsonthebaryonverysensitively:7/23/202477Integrationtoyield:7/23/202478whereThisisbecausewehavemodeledthevisibilityfunctionVasconsistingoftwohalf-gaussianpieces:7/23/202479Theresultinganalyticspectra:7/23/202480Theelectricpolarizationspectrum:7/23/202481Themagneticpolarizationspectrum:7/23/202482Dependenceonbaryondensityb:7/23/202483Dependenceondarkenergy:7/23/202484DependenceonprimordialindexnT:7/23/202485Tobedetected:7/23/202486 works on the topics Gen.Rel.Grav.34,2155(2002)Gen.Rel.Grav.35;689(2003)Chin.Phys.Lett.20,1899(2003)Chin.Phys.Lett.21,1183（2004）Class.Quant.Grav.22,1383（2005）Chin.Phys.Lett.22,1817（2005）ChineseAstronandAstrophys29,250（2005）Class.Quant.Grav.23,3783（2006）Class.Quant.Grav.23,3405（2006）PRD.73,123509(2006)PRD.74,043503(2006)Phys.Lett.B64,69(2006).7/23/202487谢谢!Merci!7/23/202488