Has inflation fulfilled its promise?

the classical view the quantum view

“ordering” “disordering”

• unpredictability problem

Linde, Linde, Mezhlumian, PRD 50, 2456 (1994)

• persistence of memory problem

• geodesic incompleteness

• entropy problem

• transplanckian problem

Either:

- solve these problems, or

- seek alternative models that avoid them

Observers & experimentalists will help:

- conduct tests that enable us to distinguishamong inflation and its alternatives

Hsmoothing > Hnormal >> Htoday

1) Inflation is fast

2) Quantum physics is random

Hsmoothing << HnormalSuppose

• Unpredictability

• Persistence of Memory

• Entropy Problem

• Singularity Problem

?

How do we go from small H to large H ?

)(4 pGH

a bounce

i.e., confront the singularity rather than ignore it

inflaton38

382

26

2

4

0

3

0

... ak

aaG

aG rmH

w ~ -1

Inflation: ultra-rapid expansion

)1(3/2~)( wtta

)1(3

0

38

a

G

w w >> 1

N.B. Do not need finely tuned initial conditions or inflation or dark energy …

ekpyrotic/cyclic: ultra-slow contraction

inflaton38

382

26

2

4

0

3

0

... ak

aaG

aG rmH

)1(3/2)(~)( wtta

Erickson, Wesley, PJS. TurokErickson, Gratton, PJS, Turok

)1(3

0

38

a

G

w w >> 1

… and avoid chaotic mixmaster behavior …

ekpyrotic/cyclic: slow contraction

inflaton38

382

26

2

4

0

3

0

... ak

aaG

aG rmH

Erickson, Wesley, PJS. TurokErickson, Gratton, PJS, Turok

)1(3

0

38

a

G

w w >> 1

… and makes scale-invariant perturbations of scalar fields …

ekpyrotic/cyclic: slow contraction

inflaton38

382

26

2

4

0

3

0

... ak

aaG

aG rmH

Erickson, Wesley, PJS. TurokErickson, Gratton, PJS, Turok

)1(3

0

38

a

G

w w >> 1

… without encountering transplanckian fluctuations.

ekpyrotic/cyclic: slow contraction

inflaton38

382

26

2

4

0

3

0

... ak

aaG

aG rmH

Erickson, Wesley, PJS. TurokErickson, Gratton, PJS, Turok

V

inflation

ekpyrotic/cyclic

V

1~)(

)(2

21

221

V

Vw

1)(

)(2

21

221

V

Vw

Khoury, PJS, Ovrut, TurokBuchbinder, Khoury, Ovrut

“bang”

radiation

matter

dark energy

“ekpyrotic”contraction

“crunch”

How do we convert scalar field fluctuationsinto curvature perturbations?

Entropic approach:two ordinary scalar fields and NO extra dimensions:

entropic curvature

Buchbinder, Khoury Ovrut,Creminelli and SenatoreKoyama, Mizumo, WandsWesley and Tolley,

Finelli & BrandenbergerLehners, McFadden, Turok, and PJS

AdS/CFT approach: (see Turok’s talk)

Turok, Craps, Hertog

• Gravitational waves?

• Non-gaussian fluctuations?

• Gravitational waves?

• Non-gaussian fluctuations?

Primordial amplitude proportional to Hsmoothing2

from Baumann, PJS, Takahashi, Ichikisee also Mollerach, Harari, Mattarese

Ananda, Clarkson, Wands

• Gravitational waves?

• Non-gaussian fluctuations?

Buchbinder, Khoury Ovrut, arXiv:0706.3903Creminelli and Senatore, hep-th/0702165

Koyama, Mizumo, Wands, to appear

wVfNL 3~''~

Entropic mechanism can producesignificant non-gaussianity:

36100 observedNLf (WMAP team)

27147 observedNLf (Yadav & Wandelt)

compatible for w < 30

conversionduring ekpyrotic

phase

J-L. Lehners & PJS

50200 NLf

Entropic mechanism can producesignificant non-gaussianity:

36100 observedNLf (WMAP team)

27147 observedNLf

conversionafter ekpyrotic

phase

compatible for w < 3000 and with tilt

(Yadav & Wandelt)

36100 observedNLf (WMAP team)

27147 observedNLf (Yadav & Wandelt)