1, The electroweak Sphaleron violates B+L and will make as low as 100GeV, M should be GeV 2, If M is higher, e.g., GUT scale or Planck mass scale, the generated baryon number asymmetry would be very small compared with the observation. In this case we need leptogenesis Comments:
ML, J. Xia, H. Li & X. Zhang, PLB (2007)
the decoupling temperature of B-L violating interaction. Sphaleron conserves B-L and converts B-L asymmetry generated above to a same order of baryon number asymmetry.
Electromagnetic anomaly Generate cosmic birefringence, may be detected by astrophysics and CMB
The action integral is gauge invariant. Cosmological CPT violation and cosmic birefringence In flat space
Geometric Optics Approximation In curved spacetime Basic equations:
Stokes parameters I→ intensity Q&U→ linear polarization V→ circular polarization The polarization angle: Spin 2
In curved spacetime, introduce tetrads
Cosmic birefringence: rotation of the polarizaton direction Rotation angle
Test CPT with CMB Polarization Experiments
Spherical multi-pole expansion Power spectra
ScalarTensorr=0.22 Challinor & Peiris (2009) TB, EB vanish in standard LCDM model
E-mode polarization, first detected by DASI 2002
For homogeneous rotation angle Power spectra changed by cosmic birefringence
Without CPT violation, the correlations of TB and EB vanish Consider the rotation angle as a free parameter
CMBPol can detect Simulation result : Current Status
4) 5) 7) J.Q.Xia et al., A&A (2008) 6)J.Q.Xia et al., ApJL(2008) Komatsu et al., arXiv: , 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: , ApJ(2009) Komatsu et al., arXiv: ) WMAP Group
WMAP7+B03+BICEP WMAP7+B03+BICEP+QUaD Jun-Qing Xia, Hong Li & Xinmin Zhang, PLB (2010) WMAP5+B03+BICEP
Comparison with laboratory CPT test Laboratory: spin-polarized torsion pendulum experiments To electrons Consider the velocity of the earth relative to the CMB rest frame Heckel et al. (2008) CMB polarization:
Explicit and spontaneous CPT violations Explicit: Gravitational field equation Einstein tensor symmetric and Inconsistent!
Constraint ML, Y. Cai, X. Wang & X. Zhang, PLB(2009)
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.
Spontaneous: Not necessary to modify the gravity! Rotation angle depends on time as well as space
Spatial dependent rotation angle: ML & X. Zhang, PRD(2008)
A new method to produce B-mode polarization CPT violation Weak gravitational lensingW.Hu 2000
Recent progresses (1)How to De-Rotate the Cosmic Microwave Background Polarization. Marc Kamionkowski, Phys.Rev.Lett.102:111302,2009. arXiv: Marc Kamionkowski (2)Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization. Amit P.S. Yadav et al, Phys.Rev.D79:123009,2009. arXiv: Amit P.S. Yadav (3) De-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism. Vera Gluscevic, Marc Kamionkowski, Asantha Cooray,Phys.Rev.D80:023510,2009. Vera GluscevicMarc KamionkowskiAsantha Cooray arXiv: (4) Non-Uniform Cosmological Birefringence and Active Galactic Nuclei. Marc Kamionkowski, Phys.Rev.D82:047302,2010. arXiv: Marc Kamionkowski (5) Cross-Correlation of Cosmological Birefringence with CMB Temperature. Robert R. Caldwell, Vera Gluscevic, Marc Kamionkowski,arXiv: Robert R. CaldwellVera GluscevicMarc Kamionkowski Reconstruct the rotation angle
Conclusions CPT violation in the early universe can be large enough to produce the observed matter-antimatter asymmetry and cosmic birefringence. Current CMB polarization experiments can be used to test CPT with high precision. CPT violation provides a new approach to produce B- mode polarization at late time.