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

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

4. The current universe is accelerated expanding
which we straightly see.

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

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

7. 1、How to solve the problems of “big bang” model

8. 1、How to solve the problems of “big bang” model

9. 1、How to solve the problems of “big bang” model

10. 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

11. 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

12. 1、How to solve the problems of “big bang” model
There are infinite possible evolutions

13. 1、How to solve the problems of “big bang” model
ln(1/a|H|)
ln(a)
“big bang” model

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

15. 2、How to have a scale invariant primordial
perturbation
Is the scale invariance of
primordial perturbation
the unique prediction of inflation ?

16. 2、How to have a scale invariant primordial
perturbation
The curvature perturbation
The equation of perturbation is

17. 2、How to have a scale invariant primordial
perturbation
The initial condition

18. 2、How to have a scale invariant primordial
perturbation
The solution is
The power spectrum is

19. 2、How to have a scale invariant primordial
perturbation
The scale invariance requires
The definition of both modes is

20. 2、How to have a scale invariant primordial
perturbation
When all are unchanged, only a
inflation contraction with w=0
Brandenberger call “matter bounce”

21. 2、How to have a scale invariant primordial
perturbation
However, the case might be inverse,
all are unchanged, only Q
Thus

22. 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.

23. 2、How to have a scale invariant primordial
perturbation

24. 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.

25. 2、How to have a scale invariant primordial
perturbation
the slow expansion scenario

26. 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, (2011)

27. 2、How to have a scale invariant primordial perturbation
Z.G.Liu, J.Zhang, Y.S.Piao, Phys.Rev.D84, (2011)

28. 2、How to have a scale invariant primordial perturbation
Y.S.Piao, Phys.Lett.B701, 526 (2011)

29. 2、How to have a scale invariant primordial
perturbation

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

31. 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.

32. “Pre big bang” scenario
The contraction with =3

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

34. 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.

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