宇宙微波背景辐射与CPT破坏

1、宇宙微波背景辐射与CPT破坏李明哲李明哲南京大学物理学院南京大学物理学院南大南大-紫台紫台 粒子粒子-核核-宇宙学联合研究中心宇宙学联合研究中心2010.4.18 南昌南昌 中国高能物理学会中国高能物理学会OutlinenBrief review on CMB polarizationnHow to test CPT violation with CMB polarizationnCurrent statusnExplicit and spontaneous CPT violationsnConclusionsBrief Review on CMB PolarizationTemperatur

2、e fluctuation at LSSlmlmlmTnYanT)()(,*,mmllTTllmTmlTCaaTemperature Angular Power SpectrumGenerating CMB polarization at LSSddTBoth density perturbation (scalar perturbation) and gravity waves (tensor perturbation) can generate quadrupole anisotropies for the radiationScalar perturbation generates T

3、and E-polarizationTensor perturbation generates T, E- and B-polarizationsPolarizations experience modifications during the propagation from LSS to the observer (reionization, weak lensing, )Here I report the change by CPT violationPolarization and Stokes parametersAt the inertial frameI intensity Q&

4、amp;U linear polarization V circular polarizationieUQiUQ222The polarization angle: QUarctan21Spin 2How To Test CPT Violation With CMB PolarizationpLorentz and CPT are violated by the Chern-Simons termThe action integral is gauge invariant if the external field is constant ormaybe the dark energy M.L

5、i, X.Wang, B.Feng, X.Zhang, PRD (2002);Li, Zhang, PLB (2003)or Ricci scalarH.Li, M.Li, X.Zhang, PRD (2004); B.Feng, H.Li, M.Li, X.Zhang, PLB(2005);M.Li, J.Xia, H.Li, X. Zhang, PLB(2007)Geometric Optics ApproximationEquations of motionBasic equations:M.Li, X.Zhang, PRD(2008)CPT violation induced the

6、rotation of the polarization directionRotation angle only depends on the difference of dark energy field at the source and the observers positions. Rotation angle characterizes the CPT-violating effect!)(fifiifdxpdkpMcp)(fiMcIIobs.constp )(fixxpBETXX,) ()2exp() () ()(11111122, 22, 2nYinYdaniUQnYdaml

7、lmmlmlobslmobslmIn the case of homogeneous lmobslmaia, 2, 2)2exp(Without CPT violation, the correlations of TB and EB vanishBo Feng, Mingzhe Li, Junqing Xia, Xuelei Chen, Xinmin Zhang, PRL(2006)Current Status0001. 0CMBPol can detectBo Feng, Mingzhe Li, Hong Li, Xinmin Zhang, PLB(2005), hep-ph/040626

8、9Simulation result:deg0 . 40 . 6WMAP3+BOOMERanG03Bo Feng, Mingzhe Li, Junqing Xia,Xuelei Chen, Xinmin Zhang, PRL(2006): 0.057 degPLANCKdeg 8 . 32 . 64)5)7)J.Q.Xia et al., A&A (2008)6)J.Q.Xia et al., ApJL(2008)Komatsu et al., arXiv:0803.0547, ApJS(2009)J.Q.Xia et al., A&A (2008)deg 0 . 35 . 2

9、deg 1 . 27 . 1deg 9 . 16 . 2P.Cabella, Natoli & Silk, PRD (2007)1) WMAP Group 3) QUaD Group deg 5 . 064. 0M.L. Brown et al., arXiv:0906.1003, ApJ(2009) deg 3 . 11 . 1Komatsu et al., arXiv:1001.45382) WMAP Group %C.L.)0.87deg(6826 . 2WMAP5+B03+BICEP%C.L.)0.36deg(680.09WMAP5+B03+BICEP+QUaDJun-Qing

10、 Xia, Hong Li & Xinmin Zhang, arXiv:0908.1876, PLB (2010)Explicit and spontaneous CPT violations.constp Explicit:FFgFgSgTFF2412021FFpTFGravitational field equation)(821FMTTGRgRG0GEinstein tensor symmetric and Inconsistent!Mingzhe Li, Yi-Fu Cai, Xiulian Wang & Xinmin Zhang, PLB(2009)4(161161R

11、RRGRGLgxqRRRR,21)(8FMTTGCGRRqC81FFGpRRq32ConstraintTB and EB on RHS are due to RRCPT violation in gravity causes different spectra for left and right handed tensorperturbations and generates TB and EB of CMB at LSS. Spontaneous:Mcp0)(TTFNot necessary to modify the gravity!McMcfi)(Rotation angle depe

12、nds on time as well as spaceEquivalence principleWe need to consider its gravitational perturbationSpatial dependent rotation angle:Mingzhe Li & Xinmin Zhang, PRD(2008)(),(40222decldeclkjkPkdkMcCConstraining a spatially dependent rotation of the Cosmic Microwave Background Polarization.Yadav, Bi

13、swas, Su, Zaldarriaga,PRD(2009)How to De-Rotate the Cosmic Microwave Background Polarization.M. Kamionkowski, PRL(2009)Detection of Spatially Dependent Rotation AngleDe-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism.V. Gluscevic, M. Kamionkowski & A. Cooray, PRD(2009)ConclusionnThe high precision CMB polarization experiments are important ways to test CPT. Currently big process mad