1. 李明哲 南京大学物理系 粒子-核-宇宙学联合研究中心
暗能量和宇宙学CPT破坏
李明哲
南京大学物理系
粒子-核-宇宙学联合研究中心

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:
Leptogenesis
Anomaly for CMB
4, Conclusion

3. Brief Review on Dark Energy
Accelerating Universe ->Dark Energy
SN Ia (SCP, HZT….)
LSS (2dfGRS, SDSS…)

4. CMB experiments

5. No antimatter
Dark matter?
Dark energy?
Why no antimatter? ……

6. Candidates: 1, Cosmological constant Negative pressure
Cosmological constant problem!
S. Weinberg, RMP (1989)

7. 2, Dynamical dark energy Flat potential 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:
crosses -1
Feng, Wang & Zhang, PLB(2005)
Li, Feng & Zhang, JCAP(2005)
Cai,Li,Lu,Piao,Qiu&Zhang, PLB(2007)
………

8. Parameterization of equation of state: A) w=w_0+w_1 z (for small z)
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)

9. Current constraint on the equation of state of dark energy
Quintom A
Quintessence
phantom
Quintom B
Xia, Li, Zhao, Zhang, PRD(2008)
WMAP5 result
E. Komatsu et al., arXiv:
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

10. Interacting Dark Energy
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
A. Long range force
Constrained tightly! S.M. Carroll, PRL(1998)
B. Instability under quantum corrections

11. 2, derivative coupling:
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
cosmological CPT violation!

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

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

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

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

16. 1, The electroweak Sphaleron violates B+L and will make
Comments:
1, The electroweak Sphaleron violates B+L and will make
as low as 100GeV, M should be GeV
Kuzmin, Rubakov&Shaposhnikov,PLB(1985)
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

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

18. 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.

19. 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

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

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

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

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

24. Basic equations:

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

26. Local Lorentz frame

29. 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!

30. Observation of cosmological CPT violation through CMB experiments

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

35. 1)
Bo Feng et al., PRL 96, (2006) 2)
WMAP3 only
P.Cabella, Natoli & Silk, PRD (2007) 3)
J.Q.Xia et al., arXiv:
WMAP5 only 4)
(WMAP Group) Komatsu et al., arXiv: 5)
J.Q.Xia et al., arXiv: 6)
J.Q.Xia et al., arXiv:

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

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

40. 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

41. Detection of Spatially Dependent Rotation Angle
How to De-Rotate the Cosmic Microwave Background Polarization. M. Kamionkowski, PRL(2009), arXiv:
Constraining a spatially dependent rotation of the Cosmic Microwave
Background Polarization. Yadav, Biswas, Su, Zaldarriaga,arXiv:

42. 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.

43. Thanks!

44. Date: Wed, 8 Oct :04: From: Marc Kamionkowski To: Zhang XinMin Subject: polarization rotation Hi Xinmin, Enclosed below is a paper that you might be interested in. It follows on work that you finished just recently. Cheers, Marc

45. From: Meng Su <mengsu@cfa. harvard. edu> To: xmzhang@mail. ihep
From: Meng Su To: Date: , 15:32:45 Subject: Greetings from Meng Su Dear Prof. Zhang This is Su Meng if you still remember:) Now I'm studying at Harvard University working with Prof. Matias Zaldarriaga. Haven't met you for a while, how is everything going with you? Recently you had a work with Dr. Li Minzhe about spacial dependent rotation of CMB polarization. I thought it is very interesting! I wrote an to Dr. Li but didn't get reply... So Kamionkowski after then had a work about reconstruct the rotation field from CMB polarization. I suggested people here to work on this topic and we just have a paper online arXiv: First of all, I hope this paper cite your previous papers on this topics well:) …………………………. Best regards, Meng Su