![Page 1: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/1.jpg)
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
![Page 2: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/2.jpg)
![Page 3: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/3.jpg)
Abstract
1 、 How to solve the problems of “big bang” model
2 、 How to have a scale invariant primordial perturbation 3 、 Comments
![Page 4: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/4.jpg)
1 、 How to solve the problems of “big bang” model
![Page 5: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/5.jpg)
1 、 How to solve the problems of “big bang” model
![Page 6: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/6.jpg)
1 、 How to solve the problems of “big bang” model
![Page 7: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/7.jpg)
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
![Page 8: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/8.jpg)
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
![Page 9: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/9.jpg)
There are infinite possible evolutions
1 、 How to solve the problems of “big bang” model
![Page 10: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/10.jpg)
1 、 How to solve the problems of “big bang” model
ln(a)
ln(1/a|H|)
“big bang” model
![Page 11: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/11.jpg)
expansion
contraction
1 、 How to solve the problems of “big bang” model
![Page 12: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/12.jpg)
Is the scale invariance of
primordial perturbation
the unique prediction of inflation ?
2 、 How to have a scale invariant primordial perturbation
![Page 13: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/13.jpg)
The curvature perturbation
2 、 How to have a scale invariant primordial perturbation
The equation of perturbation is 2
2
14
v
![Page 14: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/14.jpg)
2 、 How to have a scale invariant primordial perturbation
The initial condition
1
2 ik
ku ek
![Page 15: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/15.jpg)
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
![Page 16: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/16.jpg)
The scale invariance requires
The definition of both modes is
2 、 How to have a scale invariant primordial perturbation
![Page 17: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/17.jpg)
inflation contraction with w=0 Brandenberger call “matter bounce”
When all are unchanged, only
a
2 、 How to have a scale invariant primordial perturbation
![Page 18: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/18.jpg)
However, the case might be inverse,all are unchanged, only
Q
Thus
2 、 How to have a scale invariant primordial perturbation
![Page 19: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/19.jpg)
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
![Page 20: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/20.jpg)
2 、 How to have a scale invariant primordial perturbation
![Page 21: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/21.jpg)
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.
![Page 22: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/22.jpg)
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
![Page 23: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/23.jpg)
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
![Page 24: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/24.jpg)
Z.G.Liu, J.Zhang, Y.S.Piao, Phys.Rev.D84, 063508 (2011)
2 、 How to have a scale invariant primordial perturbation
![Page 25: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/25.jpg)
Y.S.Piao, Phys.Lett.B701, 526 (2011)
2 、 How to have a scale invariant primordial perturbation
![Page 26: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/26.jpg)
2 、 How to have a scale invariant primordial perturbation
![Page 27: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/27.jpg)
Piao, Phys.Rev.D72, 103513 (2005); Phys.Lett.B659, 839 (2008)
![Page 28: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/28.jpg)
expansion
contraction
2 、 How to have a scale invariant primordial perturbation
but inflation has the least problems.
![Page 29: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/29.jpg)
2 、 How to have a scale invariant primordial perturbation
![Page 30: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/30.jpg)
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
![Page 31: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/31.jpg)
“Pre big bang” scenario
The contraction with =3
![Page 32: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/32.jpg)
2 、 How to have a scale invariant primordial perturbation
The “curvaton” perturbation
The scale invariance requires
*
1a Q
The curvature perturbation
![Page 33: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/33.jpg)
2 、 How to have a scale invariant primordial perturbation
![Page 34: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/34.jpg)
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
![Page 35: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/35.jpg)
The scale invariance of spectrum requires
*
1a Q
for entropy mode
The problems of “big bang” model requires
*
1| |a H
| | Q H
![Page 36: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/36.jpg)
![Page 37: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/37.jpg)
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.
![Page 38: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/38.jpg)
The tensor perturbation
The scale invariance requires
Appendix How to have completely same scalar and tensor perturbation ?
![Page 39: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/39.jpg)
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 ?
![Page 40: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/40.jpg)
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 ?
![Page 41: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/41.jpg)
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 ?
![Page 42: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/42.jpg)
Y.S. Piao, arXiv:1112.3737
Appendix How to have completely same scalar and tensor perturbation ?
![Page 43: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/43.jpg)
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.
![Page 44: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/44.jpg)
How to distinguish inflation and its alternatives ?
Directly recording the time dependence of a
Xingang Chen, arXiv:1104.1323
![Page 45: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/45.jpg)
Inflation “might” be the simplest scenario of early universe. Identifying it is a challenging issue.
There are many things to do.
![Page 46: Why there are many alternatives to inflation ? Why there are many alternatives to inflation ? 朴云松 朴云松 Graduated University of CAS Graduated University](https://reader031.vdocuments.mx/reader031/viewer/2022012317/56649e915503460f94b96134/html5/thumbnails/46.jpg)
CFT
Thank Thank YouYou ! !