暗能量和宇宙學(xué)CPT破壞PPT教案

1、會計學(xué)1暗能量和宇宙學(xué)暗能量和宇宙學(xué)CPT破壞破壞SN Ia (SCP, HZT.)LSS (2dfGRS, SDSS)Brief Review on Dark EnergyAccelerating Universe -Dark Energy第1頁/共44頁CMB experiments第2頁/共44頁Dark matter?Dark energy?Why no antimatter?No antimatter第3頁/共44頁Candidates:1, Cosmological constant/1wp Cosmological constant problem! 41234310)10(pl

2、meVgT0)3(34pGaa 3/1/pwNegative pressureS. Weinberg, RMP (1989)第4頁/共44頁2, Dynamical dark energy21()( )2LV221/ 21/ 2VwVQuintessence:11w 0w Phantom:21()( )2LV 1w eVHVmeff33010)( K-essence:(, )LL 1,1ww Cannot cross -1, no-go theoremFeng, Wang & Zhang, PLB(2005);Vikman, PRD(2005);Zhao, Xia, Li, Feng

3、& Zhang, PRD(2005); Xia, Cai, Qiu, Zhao &Zhang, IJMPD(2008) Quintom: 22121211()()( ,)22LV Feng, Wang & Zhang, PLB(2005)22221()()( )2cLVMLi, Feng & Zhang, JCAP(2005)wcrosses -1 Flat potential22221()()( )2cLVM21)( VLCai,Li,Lu,Piao,Qiu&Zhang, PLB(2007)第5頁/共44頁It is important to dete

4、rmine w of DE by cosmological observations!Parameterization of equation of state: A) w=w_0+w_1 z (for small z)B) w=w_0+w_1 z / (1+z) (used mostly in the literature)C) w=w_0+w_1 sin(w_2 ln(a)+w_3)第6頁/共44頁Current constraint on the equation of state of dark energyWMAP5 resultE. Komatsu et al., arXiv:08

5、03.0547Xia, Li, Zhao, Zhang, PRD(2008)Status: 1) Cosmological constant fits data well;2) Dynamical model not ruled out;3) Best fit value of equation of state: slightly w across -1 Quintom modelQuintessencephantomQuintom AQuintom B第7頁/共44頁Dynamical dark energy is expected to have interactions to the

6、rest of the world besides the gravity.Two types of couplings: direct & derivative1, direct coupling,.),(GGFFLMceVm3310)(104plMMcA. Long range forceConstrained tightly! S.M. Carroll, PRL(1998)B. Instability under quantum correctionsmeVMm72104ewplMM ,第8頁/共44頁2, derivative coupling:cosmological CPT

7、 violation!1, obeys the shift symmetry which guarantees the flatness of the potential. 2, propagates spin-dependent force, short range, much weaker constraint from astrophysics PDG(2002)Violates Lorentz and CPT symmetry because.const00,.),(GFOMc00101)()()()(OCPTOCPTCPTOCPTGeVM1010第9頁/共44頁1010nnnnnnn

8、bbbBsn Cosmological CPT violation and baryogenesisThe universe is not symmetric between matter and antimatterWe need baryogenesisBaryon number non-conserving interactionC and CP violationsDeparture from thermal equilibrium Sakharov conditions for baryogenesis: Precondition: CPT is conserved!Cohen &a

9、mp; Kaplan, PLB(1987)第10頁/共44頁 Interacting dark energy and baryogenesisA unified picture of matter-antimatter asymmetry and dark energy!第11頁/共44頁Albrecht & Skordis, PRL(2000) )exp()()(plMfVQuintessence model with tracking solutionCopeland, Liddle & Wands, PRD(1998). 第12頁/共44頁2,100bsggg100,10

10、22Bean, Hansen & Melchiorri, PRD(2001);Doran & Robbers, JCAP(2006)第13頁/共44頁1, The electroweak Sphaleron violates B+L and will makeas low as 100GeV, M should be GeVKuzmin, Rubakov&Shaposhnikov,PLB(1985)DT10102, If M is higher, e.g., GUT scale or Planck mass scale, the generated baryon num

11、ber asymmetry would be very small compared with the observation. 3, In this case, we turn to leptogenesis Comments:第14頁/共44頁Mingzhe Li, Jun-Qing Xia, Hong Li, Xinmin Zhang, PLB (2007)iJMcL第15頁/共44頁MTsnDLB210the decoupling temperature of B-L violating interaction. DTSphaleron conserves B-L and conver

12、ts B-L asymmetry generated above to a same order of baryon number asymmetry.GeVTMMDplanck1010,第16頁/共44頁Baryon isocurvature perturbationAdiabatic or isothermal:Isocurvature or entropy: nnssnnsnXXX , 0)/(0)/(snXsnBIn our caseThe fluctuation of the dark energy scalar field will induce a nonzero baryon

13、isocurvature perturbation第17頁/共44頁)exp()()(plMfVThe quintessence model with potential )()(212/1kJCkJC510)(planckinreisocurvatuBBMHnnConsistent with the observations!第18頁/共44頁MGeVMV2230010In our model of baryo/leptogenesisThe CPT violation is very small, was large to generate enough baryon number asy

14、mmetry in the early universe.第19頁/共44頁This CPT violation can be observed by CMB polarization experiments!iJMcL第20頁/共44頁The full lagrangian of photonsThe action integral is gauge invariant.Geometric Optics Approximation第21頁/共44頁Basic equations:第22頁/共44頁Polarization and Stokes parametersAt the inertia

15、l frameI intensity Q&U linear polarization V circular polarizationieUQiUQ222The polarization angle: QUarctan21第23頁/共44頁Local Lorentz frame第24頁/共44頁第25頁/共44頁第26頁/共44頁CPT violation induced the rotation of the polarization directionRotation angle only depends on the difference of dark energy field

16、at the source and the observers positions. Which characterize such CPT-violating effect!)(fifiifdxpdkpMcpem32第27頁/共44頁第28頁/共44頁In the case of homogeneous Without CPT violation, the correlations of TB and EB vanish第29頁/共44頁第30頁/共44頁第31頁/共44頁第32頁/共44頁WMAP3 only: 0.057 degPLANCKdeg 0 . 40 . 6deg 8 . 32

17、 . 61)2)3)6)Bo Feng et al., PRL 96, 221302 (2006)5)4)(WMAP Group) Komatsu et al., arXiv:0803.0547WMAP5 onlydeg 0 . 35 . 2deg 1 . 27 . 1deg 9 . 16 . 2P.Cabella, Natoli & Silk, PRD (2007)第33頁/共44頁Spatial dependent rotation angle:Mingzhe Li & Xinmin Zhang, PRD(2008)第34頁/共44頁第35頁/共44頁第36頁/共44頁Th

18、is is the direct consequence of invariance of under the rotation sin,obsEBlobsTBlCCOnly the background evolution of dark energy provides CPT violation!第37頁/共44頁The corrections are at the order of 2In the quintessence model with tracking potential, )()(212/1kJCkJC2222)10(MeVBy assuming the initial fluctuation of quintessence generated from a GUT scale inflation第38頁/共44頁Constraining a spatially dependent rotation of the Cosmic Microwave Backgr