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Test CPT with CMB Mingzhe Li Department of Physics, Nanjing University May 10, 2011 IHEP Beijing

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Outline Cosmological CPT violation Test CPT with CMB polarization experiments Explicit and spontaneous CPT violations Conclusions

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CPT theorem: any local and Lorentz covariant quantum field theory with hermitian Hamiltonian must have CPT symmetry. ccosmoccosmo Cosmological CPT violation Cosmological CPT Violation

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Cosmological CPT violation & baryogenesis : dark energy curvature ML, X. Wang, B. Feng & X. Zhang, PRD(2002), ML & X. Zhang, PLB(2003), Davoudiasl et al, PRL(2004) H. Li, ML & X. Zhang, PRD(2004)

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Albrecht & Skordis, PRL(2000) Quintessence model with tracking solution Copeland, Liddle & Wands, PRD(1998).

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Bean, Hansen & Melchiorri, PRD(2001); Doran & Robbers, JCAP(2006)

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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:

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ML, J. Xia, H. Li & X. Zhang, PLB (2007)

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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.

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Electromagnetic anomaly Generate cosmic birefringence, may be detected by astrophysics and CMB

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The action integral is gauge invariant. Cosmological CPT violation and cosmic birefringence In flat space

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Geometric Optics Approximation In curved spacetime Basic equations:

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Stokes parameters I→ intensity Q&U→ linear polarization V→ circular polarization The polarization angle: Spin 2

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In curved spacetime, introduce tetrads

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Cosmic birefringence: rotation of the polarizaton direction Rotation angle

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Test CPT with CMB Polarization Experiments

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Spherical multi-pole expansion Power spectra

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ScalarTensorr=0.22 Challinor & Peiris (2009) TB, EB vanish in standard LCDM model

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E-mode polarization, first detected by DASI 2002

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For homogeneous rotation angle Power spectra changed by cosmic birefringence

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Without CPT violation, the correlations of TB and EB vanish Consider the rotation angle as a free parameter

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CMBPol can detect Simulation result : Current Status

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WMAP3+BOOMERanG03

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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

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WMAP7+B03+BICEP WMAP7+B03+BICEP+QUaD Jun-Qing Xia, Hong Li & Xinmin Zhang, PLB (2010) WMAP5+B03+BICEP

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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:

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Explicit and spontaneous CPT violations Explicit: Gravitational field equation Einstein tensor symmetric and Inconsistent!

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Constraint ML, Y. Cai, X. Wang & X. Zhang, PLB(2009)

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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.

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Spontaneous: Not necessary to modify the gravity! Rotation angle depends on time as well as space

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Spatial dependent rotation angle: ML & X. Zhang, PRD(2008)

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A new method to produce B-mode polarization CPT violation Weak gravitational lensingW.Hu 2000

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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

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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.

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Thanks!

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