Why there are many alternatives to inflation ? 朴云松 Graduated University of CAS USTC Hefei，2012.6.7

Inflation solve many problems of ``big bang” model, is the popular paradigm of the early universe.

The current universe is accelerated expanding which we straightly see.

Whether the early universe is accelerated expanding which we can not straightly see.

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

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

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

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

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

contraction expansion 1、How to solve the problems of “big bang” model expanding phase contracting phase 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

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

contraction expansion 2、How to have a scale invariant primordial perturbation contraction expanding phase contracting phase expansion

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.

“Pre big bang” scenario The contraction with =3

contraction expansion 2、How to have a scale invariant primordial perturbation contraction expanding phase contracting phase expansion

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.

Thanks! The end Inflation “might” be the simplest scenario of early universe. Identifying it is a challenging issue. Thanks!