1. Cosmological CPT Violation, Baryo/leptogenesis and CMB Polarization Mingzhe Li Nanjing University

2. Outline 1, Brief review on dark energy models, cosmological constant or dynamical dark energy, current status 2, Interacting dark energy: direct coupling: propagates long range force, spoils the flatness of the potential of dark energy derivative coupling: spin-dependent force, shift symmetry, guarantee the flatness of the potential, cosmological CPT violation 3, Model: LeptogenesisAnomaly for CMB 4, Conclusion

3. Brief Review on Dark Energy Models Negative pressure Candidates: 1, Cosmological constant Cosmological constant problem!

4. 2, Dynamical dark energy Quintessence: Phantom: K-essence: Cannot cross -1, no-go theorem Feng, Wang & Zhang, PLB(2005);Vikman, PRD(2005);Zhao, Xia, Li, Feng & Zhang, PRD(2005); Xia, Cai, Qiu, Zhao &Zhang, IJMPD(2008) Quintom: Feng, Wang & Zhang, PLB(2005) Li, Feng & Zhang, JCAP(2005) crosses -1 ……… Flat potential

5. It is important to determine w of DE by cosmological observations! Parameterization of equation of state: A) w=w_0+w_1 z (for small z) B) w=w_0+w_1 z / (1+z) (used mostly in the literature) C) w=w_0+w_1 sin(w_2 ln(a)+w_3)

6. Current constraint on the equation of state of dark energy WMAP5 result E. Komatsu et al., arXiv:0803.0547 Xia, Li, Zhao, Zhang, PRD(2008) Status: 1) Cosmological constant fits data well; 2) Dynamical model not ruled out; 3) Best fit value of equation of state: slightly w across -1  Quintom model Quintessence phantom Quintom A Quintom B

7. Dynamical dark energy is expected to have interactions to the rest of the world besides the gravity. Two types of couplings: direct & derivative 1, direct coupling Interacting Dark Energy A. Long range force Constrained tightly! S.M. Carroll, PRL(1998) B. Instability under quantum corrections

8. 2, derivative coupling: cosmological CPT violation! 1, obeys the shift symmetry which guarantees the flatness of the potential. 2, propagates spin-dependent force, short range, much weaker constraint from astrophysics PDG(2002) Violates Lorentz and CPT symmetry because

9. Cosmological CPT violation and baryogenesis The universe is not symmetric between matter and antimatter We need baryogenesis Baryon number non-conserving interaction C and CP violations Departure from thermal equilibrium Sakharov conditions for baryogenesis: Precondition: CPT is conserved! Cohen & Kaplan, PLB(1987)

10. Interacting dark energy and baryogenesis A unified picture of matter-antimatter asymmetry and dark energy!

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

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

13. 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. 3, In this case, we turn to leptogenesis Comments:

14. Mingzhe Li, Jun-Qing Xia, Hong Li, Xinmin Zhang, PLB (2007) The Model

15. 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.

16. Baryon isocurvature perturbation Adiabatic or isothermal: Isocurvature or entropy: In our case The fluctuation of the dark energy scalar field will induce a nonzero baryon isocurvature perturbation

17. The quintessence model with potential Consistent with the observations!

18. In our model of baryo/leptogenesis The CPT violation is very small, was large to generate enough baryon number asymmetry in the early universe.

19. This CPT violation can be observed by CMB polarization experiments!

20. The full lagrangian of photons The action integral is gauge invariant. Geometric Optics Approximation

21. Basic equations:

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

23. Local Lorentz frame

26. 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. Which characterize such CPT-violating effect!

27. Observation of cosmological CPT violation through CMB experiments

28. In the case of homogeneous Without CPT violation, the correlations of TB and EB vanish

32. WMAP3 only 1) 2) 3) 6) Bo Feng et al., PRL 96, 221302 (2006) J.Q.Xia et al., arXiv:0710.3325 5)J.Q.Xia et al., arXiv:0803.2350 4) (WMAP Group) Komatsu et al., arXiv:0803.0547 WMAP5 only J.Q.Xia et al., arXiv:0710.3325 P.Cabella, Natoli & Silk, PRD (2007)

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

36. This is the direct consequence of invariance ofunder the rotation Only the background evolution of dark energy provides CPT violation!

37. The corrections are at the order of In the quintessence model with tracking potential, By assuming the initial fluctuation of quintessence generated from a GUT scale inflation

38. Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization. Yadav, Biswas, Su, Zaldarriaga,arXiv:0902.4466 How to De-Rotate the Cosmic Microwave Background Polarization. M. Kamionkowski, arXiv:0810.1286 Detection of Spatially Dependent Rotation Angle

39. Conclusion Dynamical dark energy has possible couplings besides gravity to other matter. Direct couplings are constrained tightly. Derivative couplings are more likely. The derivative couplings violate CPT cosmologically and can explain the matter-antimatter asymmetry. Our model of leptogenesis predicts CPT violation in the photon sector. It can be tested by CMB, current data favored nonzero rotation angle mildly. The rotation angle is anisotropic in general. More studies in the future.

40. Thanks!

41. Brief review on dark energy CMB experiments

42. SN Ia (SCP, HZT….) Accelerating Universe Dark Energy LSS (2dfGRS, SDSS…)

43. Einstein Equation ： Dark energy: negative pressure

44. The corrections are at the order of The corrections can be ignored if M is above Adiabatic perturbation