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

7. Why flat Why honogeneous Why primordial perturbation ?? Thus, all problems share same origin a|H| is decreasing

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

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

10. ln(a) ln(1/a|H|) “big bang” model

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

30. 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”. 2 、 How to have a scale invariant primordial perturbation

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

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

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

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

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

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

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

40. 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) Appendix How to have completely same scalar and tensor perturbation ?

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

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

43. slow evolution inflation The exact duality Appendix How to have completely same scalar and tensor perturbation ? 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. CF T Thank You !