why there are many alternatives to inflation ?
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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!
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