[PPT] - Reheating of the universe after inflation with f( )R gravity PowerPoint Presentation

SLIDE 1

COSMO 08, Madison, 28 Aug. 2008

Reheating of the universe after inflation with f(φ φ φ φ)R gravity

Yuki Watanabe (Univ. of Texas, Austin) with Eiichiro Komatsu Based on PRD 75, 061301 (2007), [arXiv:qr-qc/0612120] PRD 77, 043514 (2008), [arXiv:0711.3442]

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Why Study Reheating?

The universe was left cold and empty after inflation.
But, we need a hot Big Bang cosmology.
The universe must reheat after inflation.

Successful inflation must transfer energy in inflaton to radiation, and heat the universe to at least ~1 MeV for successful nucleosynthesis. …however, little is known about this important epoch….

SLIDE 3

Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Why Study Reheating?

The universe was left cold and empty after inflation.
But, we need a hot Big Bang cosmology.
The universe must reheat after inflation.

Successful inflation must transfer energy in inflaton to radiation, and heat the universe to at least ~1 MeV for successful nucleosynthesis. …however, little is known about this important epoch…. Outstanding Questions

Can one reheat universe successfully/naturally?
How much do we know about reheating?
What can we learn from observations (if possible at all)?
Can we use reheating to constrain inflationary models?
Can we use inflation to constrain reheating mechanism?

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Standard Picture

) (φ V

Slow-roll Inflation:

potential shape is arbitrary here, as long as it is flat.

φ inflaton

Oscillation Phase:

around the potential minimum at the end of inflation

inf 2 2 inf 2 4 inf 4 4

~ ~ ) ( ~ ~ H M g T H M g V g T

Pl rh Pl rh rad

φ

ρ

Energetics: What determines “energy-conversion efficiency factor”, g?

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Perturbative Reheating

Dolgov & Linde (1982); Abbott, Farhi & Wise (1982); Albrecht et al. (1982)

φ φ χ χ ψ ψ

ψ

g

χ

g

+

+ + − =

4

2 int

4 1 λφ φχ ψ ψ φ

χ ψ

g g L

Inflaton decays and thermalizes through the tree-level interactions like:

φ φ

χ ψ

Thermal medium effect

Inflaton can decay if allowed kinematically with the widths given by

Pauli blocking Bose condensate

φ

φ φ φ φ

φ

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Reheating Temperature from Energetics

) 3 (

2

= + Γ + + φ φ φ

σ

m H

tot

density.

energy the dominate products Decay 3 density. energy the dominates Inflaton 3

Γ

<

Γ

>

tot

sc

tot

sc

H H

4 2 2 2 2 2

) ( 3 ) (

tot Pl

T T g M H M t π ρ = Γ = =

2 / 3 inf −

∝ >> a H H

sc

φ

Coupling constants determine the decay width, Γ. But, what determines coupling constants?

4 * 2 2

) ( 30 3 3 ) (

rh rh tot Pl

sc

Pl rh rad

T T g H M t ρ = = =

4 / 1 * 4 / 1 2

100 ) ( ) 10 (

−

Γ

=

rh tot Pl rh

T g M T π

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

What are coupling constants? Problem: arbitrariness of the nature of inflaton fields

Inflation works very well as a concept, but we do not understand

the nature (including interaction properties) of inflaton.

Arbitrariness of inflaton = Arbitrariness of couplings

e.g. Higgs-like scalar fields, Axion-like fields, Flat directions, RH sneutrino, Moduli fields, Distances between branes, and many more…

Arbitrariness of inflaton = Arbitrariness of couplings
Can we say anything generic about reheating? Universal reheating?

Universal coupling? Gravitational coupling is universal What happens to “gravitational decay channel”, when GR is modified? too weak to cause reheating with GR. In the early universe, however, GR would be modified.

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Conventional Einstein gravity during inflation

matt

L g −

2 Pl

M

φ φ

ν µ ∇

∇

( )

+

+ + − =

2 2 2 int

χ λφ φχ ψ ψ φ

χ ψ

g g L

Conventionally one introduced explicit couplings between inflaton and matter. Einstein-Hilbert term generates GR. Inflaton minimally couples to gravity.

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Modifying Einstein gravity during inflation

( )

+

+ + − =

2 2 2 int

χ λφ φχ ψ ψ φ

χ ψ

g g L

Instead of introducing explicit coupling by hand,

matt

L g −

φ φ

ν µ ∇

∇

2

) (

Pl

M v f =

Non-minimal gravitational coupling: common in effective Lagrangian from extra dimensional theories In order to ensure GR after inflation, Matter (everything but gravity and inflaton) completely decouples from inflaton and minimally coupled to gravity as usual.

) (φ V φ

v

σ

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

New decay channel through “scalar gravity waves” Fermionic (spinor) matter field:

Yukawa interaction

ψ

g

2 / 1 2 2 2

2 )] ( ' [ 3 1 ) ( ' ) ( , ) ( ~ g

−

+

= − + =

Pl Pl

M v f v f v F g M v F h g σ

µν µν µν µν

ψ ψ σ ψ γ ψ

ψ ψ µ α µα ψ 2

2 ) ( ] [

Pl

M m v F e m D e e L + + + − =

Bosonic (scalar) matter field:

Trilinear interaction

ψ

g

σ ψ

ψ

g

σ χ χ

χ

g

( )

∂

∂ + −

+

+ ∂ ∂ − = χ χ χ σ χ χ χ

ν µ µν ν µ µν χ

g U M v F U g e L

Pl

) ( 4 2 ) ( ) ( 2 1

2

)

(v F

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Magnitude of Yukawa coupling

For f(φ) = ξφ2, gψ = ξ(1+6ξ)−1/2(v/Mpl)(mψ /Mpl) Natural to obtain a small Yukawa coupling, gψ ~10-7 ,

for e.g., mψ ~10-7 Mpl

The induced Yukawa coupling vanishes for massless fermions:

σ ψ ψ

ψ

g

) (v F

The induced Yukawa coupling vanishes for massless fermions:

conformal invariance of massless fermions.

Massless, minimally-coupled scalar fields are not conformally

invariant. Therefore, the three-legged interaction does not

vanish even for massless scalar fields:

) (v F

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Decay Width Summary (Kinematical and thermal factors are neglected.) Fermions

[ ]

1 2 2 4 2 2

2 )] ( [ 3 1 32 ) (

−

′

+ ′ = Γ

pl pl

M v f M m m v f π

σ ψ

Scalar Bosons

[ ]

1 2 3 2 −

′

′

Probably the

[ ]

2 2 4 3 2

2 )] ( [ 3 1 128 ) (

′

+ ′ = Γ

pl pl

M v f M m v f π

σ

Gauge Bosons

[ ]

( )

etc fermions internal

f

# 2 )] ( [ 3 1 256 ) (

1 2 2 4 3 3 2 2

×

′

+ ′ = Γ

− pl pl

M v f M m v f π α

σ

most dominant decay channel σ

ψ

g

F F

g g

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008 4 / 1 * 2 / 3 4 / 1 2 / 1 2 2

100 ) ( ) 40 ( 8 )] ( [ 3 1 | ) ( |

<
′

+ ′

− rh pl rh pl

T g m M T M v f v f

σ

π Constraint on f(φ φ φ φ)R gravity from reheating

4 / 1 * 4 / 1 2

100 ) ( ) 10 (

−

Γ

=

rh tot Pl rh

T g M T π

FF σ

Γ +

100

pl

m M

σ 2 2

) ( ξφ φ + = M f e.g.

(c.f.) Constraints from chaotic inflation

999) Futamase(1 & Komatsu 10 5 | | ) Maeda(1989 & Futamase 10

4 3

λ ξ ξ × > − >

−

4 / 1 * 2 / 3 4 / 1 2 / 1 2 2 2

100 ) ( ) 40 ( 4 6 1 | |

<
+

− rh pl rh pl

T g m M v T M v

σ

π ξ ξ

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Worked Example: WMAP 3-yr data with Ginzburg-Landau potential

3 / 1 * 3 / 2 2 2 2 3 / 4 3 / 10 3 / 4

100 6 1 | | 1 . : ) 1 ( ~ if line black the above region the excludes 1 .

+
<

Ο <

− −

g M v M v M T M T

pl Pl Pl rh Pl rh

ξ ξ λ ξ

2 2 2

) ( ) ( v M f

pl

− + = φ ξ φ

| 10 | log

10

× λ

The theoretical parameter space allowed by the WMAP 3-yr

2 2 2

) ( 4 ) ( ) ( ) ( v V v M f

pl

− = − + = φ λ φ φ ξ φ

v = φ

allowed by the WMAP 3-yr data. Each point (red: large-field i.c., blue: small-field i.c.) shows a solution of slow-roll equations given a point of data (r, ns, ∆R2).

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Y. Watanabe, Reheating of the universe after inflation with f(phi)R gravity

COSMO 08, Madison, 28 Aug. 2008

Conclusions

A natural mechanism for reheating after inflation with

f(φ)R gravity: Why natural?

Inflaton quanta decay spontaneously into any matter fields (spin-0,

½, 1) without explicit interactions in the original Lagrangian

Conformal invariance must be broken at the tree-level or by loops Reheating spontaneously occurs in any theories with f(φ)R gravity

A constraint on f(φ) from the reheat temperature can be A constraint on f(φ) from the reheat temperature can be

found.

A possible limit on the reheat temperature can constrain the form

f f(φ), or vice versa.

These constraints on f(φ) are totally independent of the other