Why there are many Why there are many alternatives to alternatives to

inflation ?inflation ?

朴云松朴云松 Graduated University of CASGraduated 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” model2 、 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

Why flat

Why honogeneous

Why primordial perturbation

??

Thus, all problems share same origin

a|H| is decreasing

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

*

1

a

*

1| |

a H actually for any evolution

for inflationHta e

There are infinite possible evolutions

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

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

ln(a)

ln(1/a|H|)

“big bang” model

expansion

contraction

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

0 1

expanding phase

contracting phase

Is the scale invariance of

primordial perturbation

the unique prediction of inflation ?

2 、 How to have a scale invariant primordial perturbation

The curvature perturbation

2 、 How to have a scale invariant primordial perturbation

The equation of perturbation is 2

2

14

v

2 、 How to have a scale invariant primordial perturbationThe initial condition

12

ikku e

k

The solution is

2 、 How to have a scale invariant primordial perturbation

The power spectrum is

23 2

2 3 22 1 ( )

2

vk

R R

uk HP kz Q

( 1/2)

2 1/2

3/2

( ) 132 2( )2

i vv

k v

e vu kk

The scale invariance requires

The definition of both modes is

2 、 How to have a scale invariant primordial perturbation

inflation contraction with w=0 Brandenberger call “matter bounce”

When all are unchanged, only

a

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“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

2 、 How to have a scale invariant primordial perturbation

2 、 How to have a scale invariant primordial perturbationThe duality of primordial perturbations (early universe scenarios)

2

2

2

2

p

p

HPM

HPM

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 perturbationthe slow expansion scenario 1/

*( ) a t t

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

2 、 How to have a scale invariant primordial perturbation

expansion

contraction

0 1

expanding phase

contracting phase

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.

2 、 How to have a scale invariant primordial perturbation

“Pre big bang” scenario

The contraction with =3

expansion

contraction

0 1

expanding phase

contracting phase

2 、 How to have a scale invariant primordial perturbation

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.

The end

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

Thanks!