Outline n n n Brief review on CMB

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

Brief Review on CMB Polarization

Temperature fluctuation at LSS

Temperature Angular Power Spectrum

Generating CMB polarization at LSS

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

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

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)

Equations of motion Geometric Optics Approximation

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

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!

In the case of homogeneous

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

Current Status Simulation result: CMBPol can detect Bo Feng, Mingzhe Li, Hong Li, Xinmin Zhang, PLB(2005), hep-ph/0406269 WMAP 3+BOOMERan. G 03 Bo Feng, Mingzhe Li, Junqing Xia, Xuelei Chen, Xinmin Zhang, PRL(2006)

1) WMAP Group Komatsu et al. , ar. Xiv: 1001. 4538 2) WMAP Group Komatsu et al. , ar. Xiv: 0803. 0547, Ap. JS(2009) 3) QUa. D Group M. L. Brown et al. , ar. Xiv: 0906. 1003, Ap. J(2009) 4) P. Cabella, Natoli & Silk, PRD (2007) 5) J. Q. Xia et al. , A&A (2008) 6) J. Q. Xia et al. , Ap. JL(2008) 7) J. Q. Xia et al. , A&A (2008)

WMAP 5+B 03+BICEP+QUa. D Jun-Qing Xia, Hong Li & Xinmin Zhang, ar. Xiv: 0908. 1876, PLB (2010)

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

Constraint

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

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

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

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

Conclusion n 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.

Thanks!