Outline Of Topics

1. 暗能量、残余引力波、CMB极化Dark energy, relic GW and CMB polarization张杨 (Yang Zhang)中国科学技术大学 (USTC)天体物理中心(CFA)

2. Outline Of Topics • 一、 Cosmic Dark Energy • 二、 Relic Gravitational Waves • 三、 CMB Polarizations by RGW

3. 一、 Cosmic Dark Energy-- the effective YM condensate model

4. Observational Evidence for Accelerating Expansion • SN Ia型超新星 • Riess(1998) • Permutter(1999) • Tonry(2003), z=0.3~1.3, 8 new • Knop(2003), z=0.36-0.86, 11 new • CMB anisotropies (WMAP) • Large scale structure etc.

5. Models for Dark Energy:1. Cosmological constant: Λ2. Effective gravity: L = R + bR lnR +…3. scalar field：quintessence, k-essence, etc4.Bag-Model (T.D.Lee) φ =const. 5.Effective Yang-Mills condensate

6. Coincidence Problem：

7. strategy:construct a tracking solution,the present state is insensitive to the initial conditions.

8. Effective Yang-Mills condensate: Idea: What if the Universe is filled with quantum effective YM condensate as the ground state? The universe is quite similar to the QCD vacuum in hadrons, to which the quantum effective Yang-Mills condensate contributes.

9. Recall : MIT Bag Constant : Idea: Quarks inside hadrons feel a vacuum with ρ=B, p= -B, where B is MIT Bag constant. QCD vacuum in hadrons can be phenomenologically described by the B, to which the gluon condensate contributes.

11. Interesting features:quantum effective—1-loop contribution;gauge invariance; Lorentz invariance;correct trace anomaly;

13. Observe that:the effective YM condensate behaves asat high energies, py→ρy /3, radiationat low energies, py→-ρy , dark energyThis will lead to the scaling behavior, and the track solution.

14. Friedmann equation:

16. Non-interaction:

17. Interaction with matter:

18. The model 1 : i.e. the YM condensate decays into matter at the rate Г.

22. Remark: A tracker solution exists for a wide range of the initial YM energy density; The present state ΩΛ≈0.73, Ωm≈0.27 is realized naturally as a result of evolution;

23. wy =ρy/pygoes from 1/3 crosses over -1,and settles down to w< -1;Other choices of Г/H alsoyield similar evolution behavior;ρm levels off;

24. The asymptotic behavior of the tracker solution with Ωy→0.73,Ωm→ 0.27, as t →∞It is a fixed point, and it is stable .

25. Phase graph for trajectories:

26. The model 2: i.e. the matter decays into the YM condensate at a rate Г.

30. Remark: similar to the model 1 wy =ρy/pyalsogoes from 1/3, and approaches to -1, but does not go to w< -1;ρm does not level off.

31. Interaction with both Matter and Radiation:

32. Taking, for instance, the couplings as :

36. Remark: similar to the previous models. Both ρm and ρ r level off.

37. The past history of the Universe is similar to the standard Big Bang model, and yet the future Universe is a steady one, quite similar to the Steady State Model (Bondi, Gold, Hoyle, 1948).

38. Section Summary:The effective YM condensate dark energy model can solve the coincidence problem for generic interactions with matter and radiation, and for a wide range of initial values of YM density.

39. 二、 Relic GW--- in the accelerating universe driven by dark energy

40. How does the dark energy affect the spectrum of relic GW？ We have obtained the exact spectrum h(t,k) of relic GW in the accelerating Universe

41. GW: transverse and traceless wave equation:

43. the spectrum is defined by

44. the initial condition:

45. which can be fixed by CMB anisotropies on large scales:

46. various stages of expansion

47. Now add the accelerating stage:

48. connecting condition:

49. The scale factor a(t) depends the dark energy