1. 宇宙微波背景辐射与 CPT 破坏 李明哲 南京大学物理学院 南大 - 紫台 粒子 - 核 - 宇宙学联合研究中心 2010.4.18 南昌 中国高能物理学会

2. Outline Brief review on CMB polarization How to test CPT violation with CMB polarization Current status Explicit and spontaneous CPT violations Conclusions

3. Brief Review on CMB Polarization

4. Temperature fluctuation at LSS

5. Temperature Angular Power Spectrum

6. Generating CMB polarization at LSS

7. Both density perturbation (scalar perturbation) and gravity waves (tensor perturbation) can generate quadrupole anisotropies for the radiation Scalar perturbation generates T and E-polarization Tensor perturbation generates T, E- and B-polarizations Polarizations experience modifications during the propagation from LSS to the observer (reionization, weak lensing, …) Here I report the change by CPT violation

8. Polarization and Stokes parameters At the inertial frame I→ intensity Q&U→ linear polarization V→ circular polarization The polarization angle: Spin 2

9. How To Test CPT Violation With CMB Polarization Lorentz and CPT are violated by the Chern-Simons term The action integral is gauge invariant if the external field is constant or maybe the dark energy M.Li, X.Wang, B.Feng, X.Zhang, PRD (2002);Li, Zhang, PLB (2003) or Ricci scalar H.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)

10. Geometric Optics Approximation Equations of motion

11. Basic equations: M.Li, X.Zhang, PRD(2008)

12. CPT violation induced the rotation of the polarization direction Rotation angle only depends on the difference of dark energy field at the source and the observer’s positions. Rotation angle characterizes the CPT-violating effect!

14. In the case of homogeneous

15. Without CPT violation, the correlations of TB and EB vanish Bo Feng, Mingzhe Li, Junqing Xia, Xuelei Chen, Xinmin Zhang, PRL(2006)

16. Current Status CMBPol can detect Bo Feng, Mingzhe Li, Hong Li, Xinmin Zhang, PLB(2005), hep-ph/0406269 Simulation result: WMAP3+BOOMERanG03 Bo Feng, Mingzhe Li, Junqing Xia, Xuelei Chen, Xinmin Zhang, PRL(2006)

17. 4) 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) P.Cabella, Natoli & Silk, PRD (2007) 1) WMAP Group 3) QUaD Group M.L. Brown et al., arXiv:0906.1003, ApJ(2009) Komatsu et al., arXiv:1001.4538 2) WMAP Group

18. WMAP5+B03+BICEP WMAP5+B03+BICEP+QUaD Jun-Qing Xia, Hong Li & Xinmin Zhang, arXiv:0908.1876, PLB (2010)

19. Explicit and spontaneous CPT violations Explicit: Gravitational field equation Einstein tensor symmetric and Inconsistent! Mingzhe Li, Yi-Fu Cai, Xiulian Wang & Xinmin Zhang, PLB(2009)

20. Constraint

21. TB and EB on RHS are due to CPT violation in gravity causes different spectra for left and right handed tensor perturbations and generates TB and EB of CMB at LSS.

22. Spontaneous: Not necessary to modify the gravity! Rotation angle depends on time as well as space Equivalence principle We need to consider its gravitational perturbation

23. Spatial dependent rotation angle: Mingzhe Li & Xinmin Zhang, PRD(2008)

25. Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization. Yadav, Biswas, Su, Zaldarriaga,PRD(2009) How to De-Rotate the Cosmic Microwave Background Polarization. M. Kamionkowski, PRL(2009) Detection of Spatially Dependent Rotation Angle De-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism. V. Gluscevic, M. Kamionkowski & A. Cooray, PRD(2009)

26. Conclusion The high precision CMB polarization experiments are important ways to test CPT. Currently big process made along this direction. Explicit CPT breaking models need to modify the gravity. For spontaneous CPT breaking, the rotation angle is spatial dependent, we need to consider its gravitational perturbation.

27. Thanks!