Why there are many alternatives to inflation ?

1. Why there are many alternatives to inflation ? 朴云松 Graduated University of CAS Hangzhou，2012.4.11

3. Abstract 1、How to solve the problems of “big bang” model 2、How to have a scale invariant primordial perturbation 3、Comments

4. 1、How to solve the problems of “big bang” model

5. 1、How to solve the problems of “big bang” model

6. 1、How to solve the problems of “big bang” model

7. 1、How to solve the problems of “big bang” model Thus, all problems share same origin Why flat Why primordial perturbation a|H| is decreasing ?? Why honogeneous

8. 1、How to solve the problems of “big bang” model Thus, the solution is in a period of early universe, a|H| increases with time. actually for any evolution for inflation

9. 1、How to solve the problems of “big bang” model There are infinite possible evolutions

10. 1、How to solve the problems of “big bang” model ln(1/a|H|) ln(a) “big bang” model

11. 1、How to solve the problems of “big bang” model contraction expansion

12. 2、How to have a scale invariant primordial perturbation Is the scale invariance of primordial perturbation the unique prediction of inflation ?

13. 2、How to have a scale invariant primordial perturbation The curvature perturbation The equation of perturbation is

14. 2、How to have a scale invariant primordial perturbation The initial condition

15. 2、How to have a scale invariant primordial perturbation The solution is The power spectrum is

16. 2、How to have a scale invariant primordial perturbation The scale invariance requires The definition of both modes is

17. 2、How to have a scale invariant primordial perturbation When all are unchanged, only a inflation contraction with w=0 Brandenberger call “matter bounce”

18. 2、How to have a scale invariant primordial perturbation However, the case might be inverse, all are unchanged, only Q Thus

19. 2、How to have a scale invariant primordial perturbation is the slow contraction is the slow expansion Khoury, Steinhardt,et.al “Nearly scale invariant spectrum of adiabatic fluctuations may be from a very slowly expanding phase of the universe.” Phys.Rev.D68:083515,2003.

20. 2、How to have a scale invariant primordial perturbation

21. 2、How to have a scale invariant primordial perturbation The duality of primordial perturbations (early universe scenarios) for inflation for slow evolution Piao, Zhang, Phys.Rev.D70:043516,2004. Boyel, Steinhardt, Turok, Phys.Rev.D70:023504,2004.

22. 2、How to have a scale invariant primordial perturbation the slow expansion scenario distinguished from “The Emergent Universe: inflationary cosmology with no singularity” G.Ellis, R. Maartens Class.Quant.Grav.21:223-232,2004

23. 2、How to have a scale invariant primordial perturbation the evolutions with rapidly changed inflation Z.G.Liu, J.Zhang, Y.S.Piao,Phys.Rev.D84, 063508 (2011)

24. 2、How to have a scale invariant primordial perturbation Z.G.Liu, J.Zhang, Y.S.Piao,Phys.Rev.D84, 063508 (2011)

25. 2、How to have a scale invariant primordial perturbation Y.S.Piao,Phys.Lett.B701, 526 (2011)

26. 2、How to have a scale invariant primordial perturbation

27. Piao, Phys.Rev.D72, 103513 (2005); Phys.Lett.B659, 839 (2008)

28. 2、How to have a scale invariant primordial perturbation contraction expansion but inflation has the least problems.

29. 2、How to have a scale invariant primordial perturbation

30. 2、How to have a scale invariant primordial perturbation However, with the “curvaton” mechanism in principle, the perturbation can be scale invariant for arbitrary evolutions. It is applied earlier in Veneziano et.al“Pre Big Bang”.

31. “Pre big bang” scenario The contraction with =3

32. 2、How to have a scale invariant primordial perturbation The curvature perturbation The “curvaton” perturbation The scale invariance requires

33. 2、How to have a scale invariant primordial perturbation

34. 3、Why there are many alternatives to inflation ? The problems of “big bang” model requires The scale invariance of spectrum requires for adiabatic mode

35. The problems of “big bang” model requires The scale invariance of spectrum requires for entropy mode

37. How to distinguish inflation and its alternatives ? When the perturbation is Gaussian,|f_NL|<1, inflation is the simplest scenario of early universe. When there is the tensor perturbation inflation is the simplest scenario of early universe.

38. Appendix How to have completely same scalar and tensor perturbation ? The tensor perturbation The scale invariance requires

39. Appendix How to have completely same scalar and tensor perturbation ? When all are unchanged, only a inflation contraction with w=0 However, it is large, r>1.

40. Appendix How to have completely same scalar and tensor perturbation ? The scalar and tensor perturbation are conformal invariant. i.e. in conformal related frames, the results obtained are same. N.Makino, M.Sasaki, Prog. Theor. Phys 86, 103 (1991)

41. Appendix How to have completely same scalar and tensor perturbation ? We did a detailed calculation for slow expanding scenario. When a is slow expanding, only

42. Appendix How to have completely same scalar and tensor perturbation ? Y.S. Piao, arXiv:1112.3737

43. Appendix How to have completely same scalar and tensor perturbation ? The exact duality slow evolution inflation The approximate duality Piao, Zhang, Phys.Rev.D70:043516,2004. Boyel, Steinhardt, Turok, Phys.Rev.D70:023504,2004.

44. How to distinguish inflation and its alternatives ? Directly recording the time dependence of a Xingang Chen, arXiv:1104.1323

45. Inflation “might” be the simplest scenario of early universe. Identifying it is a challenging issue. There are many things to do.

46. Thank You ! CFT