1. Dark Energy Perturbations 李明哲 南京大学物理学院 2011.10.13 中国科技大学交叉学科理论研究中心 合肥

2. Outline Importance of cosmological perturbations Dark energy models Dark energy perturbations Dark energy coupling to CMB photons I Dark energy coupling to CMB photons II Conclusions

3. Importance of cosmological perturbations

4. Inflation quantum fluctuation Primordial perturbation

5. 1965 COBE WMAP CMB anisotropy

6. Tests of perturbation theory CMB Angular Power Spectrum

7. Matter Power Spectrum

8. Dark Energy (DE)

9. Accelerating universe Negative pressure 1, Cosmological Constant (Einstein 1917) No perturbation

10. Cosmological constant problem Observation Zero point energy density

11. 2, Dynamical dark energy I, quintessence Peccei, Sola, Wetterich, 1987 Wetterich, 1988 Peebles, Ratra, 1988 Zlatev, Wang, Steinhardt, 1998 II, phantom Caldwell, 1999

12. III, k-essence Amendariz-Picon, Mukhanov, Steinhardt, 2000 Quintessence, phantom are special cases of k-essence W cannot cross -1 IV, quintom w crosses -1 Feng, Wang, Zhang, 2004 ML, Feng, Zhang, 2005 Cai, ML, Lu, Piao, Qiu, Zhang, 2007

13. W a crucial parameter to distinguish different models Data fitting, model independent, parameterization DE perturbation, only vanished when w=-1 (cosmological constant) Naively switch off DE perturbation is not consistent Using observational data to search for DE models

14. Without DE perturbation With DE perturbation Weller, Lewies, 2003 Constant w and sound speed

15. FRW background Metric perturbation Equations of perturbations Conformal Newtonian Gauge Dark Energy Perturbations

16. All matter including DE contribute to the metric perturbation

17. : sound speed in the comoving frame Adiabatic sound speed Single fluid Quintessence, phantom K-essence

18. Equations of dark energy perturbation The problem of dark energy perturbations Singular when w_e crosses -1 No-Go Theorem J.Xia, Y.Cai, T.Qiu, G.Zhao, X.Zhang (2008) Quintom dark energy B.Feng, X.Wang, X.Zhang (2005) More degrees of freedom

19. Parameterization, e.g., Multi fluids or multi fields need more equations not applicable Not convenient in data analysis Method without new parameters Zhao, Xia, ML, Feng, Zhang, 2005 Quintessence like Phantom like

20. Fitting result with and without DE perturbation

21. Matching condition ML, Cai, Li, Brandenberger, Zhang, 2010 Space-like surface The induced 3-metric on and its extrinsic curvature be continuous on both sides go to the “tilde coordinate system”

22. Gauge transformation

23. Matching condition 3-metric extrinsic curvature

24. In arbitrary gauge In conformal Newtonian gauge

26. Gauge-invariant variables Initial conditions: adiabatic & isocurvature

27. Super-horizon scales

28. Adiabatic perturbation Isocurvature perturbation Mixture of adiabatic and isocurvature modes

29. Adiabatic perturbation

30. Pure dark matter isocurvature perturbation Ruled out by experiments

31. DE isocurvature perturbation Liu, ML, Zhang, 2010

34. The action integral is gauge invariant. Geometric Optics Approximation Dark energy coupling to photons I: Chern-Simons and CPT violation

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

36. Six spectra

37. CPT violation induced the rotation of the polarization direction Rotation angle characterizes the CPT-violating effect!

38. Background homogeneous

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

40. CMBPol can detect Simulation result : Current Status

41. WMAP3+BOOMERanG03

43. Perturbation, spatial dependent rotation angle ML, Zhang, 2008

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

46. Dark energy coupling to photons II: varying fine structure constant

47. Wang, ML, 2009 r: recombination

48. Linear fluctuation, new long range force

49. Weak gravitational lensing

50. Conclusions Naively turn off dark energy perturbation is not consistent. We need new method to treat the dark energy perturbation in the whole parameter space. DE isocurvature perturbation is not strongly constrained by current data, but it is expected to be limited more tightly by CMB-LSS cross correlation. In models of dark energy interacting with photons, the perturbation of dark energy has interesting implications.

51. Thanks!