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## Why there are many alternatives to inflation ?

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**Why there are many alternatives to inflation ?**朴云松 Graduated University of CAS Hangzhou，2012.4.11**Abstract**1、How to solve the problems of “big bang” model 2、How to have a scale invariant primordial perturbation 3、Comments**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**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**1、How to solve the problems of “big bang” model**There are infinite possible evolutions**1、How to solve the problems of “big bang” model**ln(1/a|H|) ln(a) “big bang” model**1、How to solve the problems of “big bang” model**contraction expansion**2、How to have a scale invariant primordial**perturbation Is the scale invariance of primordial perturbation the unique prediction of inflation ?**2、How to have a scale invariant primordial**perturbation The curvature perturbation The equation of perturbation is**2、How to have a scale invariant primordial**perturbation The initial condition**2、How to have a scale invariant primordial**perturbation The solution is The power spectrum is**2、How to have a scale invariant primordial**perturbation The scale invariance requires The definition of both modes is**2、How to have a scale invariant primordial**perturbation When all are unchanged, only a inflation contraction with w=0 Brandenberger call “matter bounce”**2、How to have a scale invariant primordial**perturbation However, the case might be inverse, all are unchanged, only Q Thus**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.**2、How to have a scale invariant primordial**perturbation**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.**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**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)**2、How to have a scale invariant primordial**perturbation Z.G.Liu, J.Zhang, Y.S.Piao,Phys.Rev.D84, 063508 (2011)**2、How to have a scale invariant primordial**perturbation Y.S.Piao,Phys.Lett.B701, 526 (2011)**2、How to have a scale invariant primordial**perturbation**Piao, Phys.Rev.D72, 103513 (2005);**Phys.Lett.B659, 839 (2008)**2、How to have a scale invariant primordial**perturbation contraction expansion but inflation has the least problems.**2、How to have a scale invariant primordial**perturbation**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”.**“Pre big bang” scenario**The contraction with =3**2、How to have a scale invariant primordial**perturbation The curvature perturbation The “curvaton” perturbation The scale invariance requires**2、How to have a scale invariant primordial**perturbation**3、Why there are many alternatives to inflation ?**The problems of “big bang” model requires The scale invariance of spectrum requires for adiabatic mode**The problems of “big bang” model requires**The scale invariance of spectrum requires for entropy mode**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.**Appendix**How to have completely same scalar and tensor perturbation ? The tensor perturbation The scale invariance requires**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.**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)**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**Appendix**How to have completely same scalar and tensor perturbation ? Y.S. Piao, arXiv:1112.3737**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.**How to distinguish**inflation and its alternatives ? Directly recording the time dependence of a Xingang Chen, arXiv:1104.1323**Inflation “might” be**the simplest scenario of early universe. Identifying it is a challenging issue. There are many things to do.**Thank You !**CFT