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

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

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

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 perturbation

The initial condition

1

2 ik

ku ek

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 k

z Q

( 1/2)

21/2

3/2

( ) 132 2( )2

i vv

k v

e vu k

k

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 perturbation

The duality of primordial perturbations (early universe scenarios)

2

2

2

2

p

p

HP

M

HP

M

for inflation

for slow evolution

Piao, Zhang, Phys.Rev.D70:043516,2004.Boyel, Steinhardt, Turok, Phys.Rev.D70:023504,2004.

distinguished from“The Emergent Universe: inflationary cosmology with no singularity” G.Ellis, R. MaartensClass.Quant.Grav.21:223-232,2004

2 、 How to have a scale invariant primordial perturbation

the slow expansion scenario1/

*( ) 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

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

expansion

contraction

2 、 How to have a scale invariant primordial perturbation

but inflation has the least problems.

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”.

2 、 How to have a scale invariant primordial perturbation

“Pre big bang” scenario

The contraction with =3

2 、 How to have a scale invariant primordial perturbation

The “curvaton” perturbation

The scale invariance requires

*

1a Q

The curvature perturbation

2 、 How to have a scale invariant primordial perturbation

The problems of “big bang” model requires

3 、 Why there are many alternatives to inflation ?

*

1| |a H

The scale invariance of spectrum requires

*

1Ra Q

for adiabatic mode

| |RQ H

The scale invariance of spectrum requires

*

1a Q

for entropy mode

The problems of “big bang” model requires

*

1| |a H

| | Q H

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 tensor perturbation

The scale invariance requires

Appendix How to have completely same scalar and tensor perturbation ?

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 ?

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 ?

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.

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.

CFT

Thank Thank YouYou ! !