1. Testing CPT with CMB 李明哲 University of Bielefeld 2008 年 4 月 28 日

2. "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation". John C. Mather & George F. Smoot

3. CMB (Maxima, Boomerang, WMAP) SN Ia (SCP, HZT,SNLS,ESSENCE) LSS (2dfGRS, SDSS) Precision Cosmology Concordance Model Inflation + Dark Matter + Dark Energy Problems: 1, What is inflaton? What happened in detail during inflation? 2, What is dark matter particle? 3, What is dark energy? 4, Why no anti-matter?

4. Outline Brief review on dark energy models Interacting dark energy, cosmological CPT violation and baryogenesis Testing CPT with CMB Summary

5. Brief review on dark energy models Einstein equation: Negative pressure and almost not cluster Candidates: 1, Cosmological constant (or vacuum energy) Cosmological constant problem! S. Weinberg, RMP(1989) 2, Dynamical fields Quintessence

6. Phantom Quintom crosses -1 Feng, Wang & Zhang, PLB(2005) Li, Feng & Zhang, JCAP(2005)

7. Phantom Quintessence Quintom A Quintom B Current constraints on dark energy models

8. No-Go Theorem For theory of dark energy (DE) in the 4D Friedmann-Robertson-Walker (FRW) universe described by a single perfect fluid or a single scalar field with a largangian of, which minimally couples to Einstein Gravity, its equation of state w cannot cross over the cosmological constant boundary. A challenge to dark energy theories Quintom models with double fields or higher derivatives can avoid this problem Zhao, Xiao, Li, Feng & Zhang, PRD(2005).

9. Interacting dark energy, cosmological CPT violation and baryogenesis Matter-antimatter asymmetry (Baryon number asymmetry) BBN, CMB, … Since Dirac, fundamental theories are not biased between matter and antimatter We need baryogenesis: the process to produce baryon number asymmetry Baryon number non-conserving interaction C and CP violations Departure from thermal equilibrium Sakharov conditions for baryogenesis: Precondition: CPT is conserved!

10. CPT Theorem If a field theory: 1) is local; 2) is Hermitian; 3) is Lorentz covariant; 4) satisfies spin-statistic relations; CPT is conserved The rolling of dark energy scalar field breaks Lorentz covariance It provides a source to violate CPT, e.g., Cosmological CPT violation

12. Generalization

14. CPT violation in photon sector; P and CP are also violated

15. Testing CPT with CMB

18. The CPT violating term is potentially observable with photons polarization

19. Polarization and Stokes parameters

20. General definition of Stokes parameters M.Li et al, work in progress

24. CMB polarization

31. P.Cabella, Natoli & Silk, PRD76, 123014 (2007) Bo Feng et al., PRL 96, 221302 (2006) J.Q.Xia et al., arXiv:0710.3325 J.Q.Xia et al., arXiv:0803.2350 (WMAP Group) Komatsu et al., arXiv:0803.0547 J.Q.Xia et al., arXiv:0710.3325 WMAP3 only 2) 1) 3) 4) WMAP5 only 5) 6)

32. Summary Precision cosmology supports the model of the universe with dark energy and current data favors slightly quintom dynamical dark energy. Interacting dark energy induces cosmological CPT violation, can be tested by CMB and current data provides a weak evidence for such a CPT violation.