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Dissipative Effects on Reheating after Inflation Kyohei Mukaida (Univ. of Tokyo) Based on: 1212.1985 , 1208.3399 with K. Nakayama ; [ JCAP01(2013)017 , JCAP03(2013)002], also 1304.6597 with T. Moroi , K. Nakayama and M. Takimoto; [

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Kyohei Mukaida - Univ. of Tokyo

1

Dissipative Effects

  • n

Reheating after Inflation

Kyohei Mukaida (Univ. of Tokyo)

Based on: 1212.1985,1208.3399 with K. Nakayama;

[JCAP01(2013)017, JCAP03(2013)002], also 1304.6597 with T. Moroi, K. Nakayama and M. Takimoto;

[JHEP1306(2013)040]

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Introduction

2

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SLIDE 3

Kyohei Mukaida - Univ. of Tokyo

Introduction

After the inflation, the inflaton should convert its energy to radiation: Reheating. How does the reheating proceed ?

3

φ

Inflaton

φ Vφ

  • “Standard” picture of reheating:
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SLIDE 4

Kyohei Mukaida - Univ. of Tokyo

Introduction

After the inflation, the inflaton should convert its energy to radiation: Reheating. How does the reheating proceed ?

4

φ

Inflaton

φ Vφ

χ ˜ χ χ

χ0, χ00 · · · Aµ

Decay Thermal Plasma

λ φ ¯ χ χ

  • “Standard” picture of reheating:
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SLIDE 5

Kyohei Mukaida - Univ. of Tokyo

  • “Standard” picture of reheating:

Introduction

After the inflation, the inflaton should convert its energy to radiation: Reheating. How does the reheating proceed ?

5

φ

Inflaton

φ Vφ

χ ˜ χ χ

χ0, χ00 · · · Aµ

Decay

@ H ∼ Γ(pert.)

φ

∼ λ2mφ

Thermal Plasma

λ φ ¯ χ χ

  • Reheating temperature:TR ∼

" 90 π2g∗ #1/4 q Mpl Γ(pert)

φ

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SLIDE 6

Kyohei Mukaida - Univ. of Tokyo

  • “Standard” picture of reheating:

Introduction

After the inflation, the inflaton should convert its energy to radiation: Reheating. How does the reheating proceed ?

6

φ

Inflaton

φ Vφ

χ ˜ χ χ

χ0, χ00 · · · Aµ

Decay

@ H ∼ Γ(pert.)

φ

∼ λ2mφ

Thermal Plasma

λ φ ¯ χ χ

  • Reheating temperature:TR ∼

" 90 π2g∗ #1/4 q Mpl Γ(pert)

φ

However... This Simple Picture does NOT ALWAYS hold !

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SLIDE 7

Kyohei Mukaida - Univ. of Tokyo

Introduction

7

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 8

Kyohei Mukaida - Univ. of Tokyo

Introduction

8

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • Before going into details, let us clarify our setup:

Lkin − 1 2m2

φφ2 + λφ (¯

χLχR + h.c.) + Lother

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 9

Kyohei Mukaida - Univ. of Tokyo

Introduction

9

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • Before going into details, let us clarify our setup:

Lkin − 1 2m2

φφ2 + λφ (¯

χLχR + h.c.) + Lother

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 10

Kyohei Mukaida - Univ. of Tokyo

Introduction

10

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • Before going into details, let us clarify our setup:

Lkin − 1 2m2

φφ2 + λφ (¯

χLχR + h.c.) + Lother

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 11

Kyohei Mukaida - Univ. of Tokyo

Introduction

11

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • Before going into details, let us clarify our setup:

Lkin − 1 2m2

φφ2 + λφ (¯

χLχR + h.c.) + Lother

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 12

Kyohei Mukaida - Univ. of Tokyo

Introduction

12

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • Before going into details, let us clarify our setup:

Lkin − 1 2m2

φφ2 + λφ (¯

χLχR + h.c.) + Lother

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

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SLIDE 13

Kyohei Mukaida - Univ. of Tokyo

Introduction

13

Missing Two effects (at least):

φ

Interaction

χ

Thermal Plasma

χ ˜ χ

Gauge int. χ0, χ00 · · ·

Aµ

Real Scalar

  • What if ??

λφ ¯ χχ; (λ2φ2| ˜

χ|2)

m2

eff,χ = λ2φ(t)2 + mth χ (T)2 ∼ g2T2

mφ

Γ(pert.)

φ

??

meff,χ

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SLIDE 14

Kyohei Mukaida - Univ. of Tokyo

Introduction

14

Missing Two effects (at least):

➡ Non-perturbative particle production (Preheating) ➡ Thermal dissipation into radiation (via Scatterings)

e.g., [L. Kofman, A. Linde, A. Starobinsky] e.g., [J. Yokoyama; M. Drewes; A. Berera et al.]

meff,χ ∼ λ ˜ φ mφ

  • 1. If

meff,χ ∼ mth

χ

  • 2. If

mφ

  • What if ??

mφ

Γ(pert.)

φ

??

meff,χ

∼ g2T2

m2

eff,χ = λ2φ(t)2 + mth χ (T)2

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SLIDE 15

Kyohei Mukaida - Univ. of Tokyo

Introduction

15

Missing Two effects (at least):

➡ Non-perturbative particle production (Preheating) ➡ Thermal dissipation into radiation (via Scatterings)

e.g., [L. Kofman, A. Linde, A. Starobinsky] e.g., [J. Yokoyama; M. Drewes; A. Berera et al.]

meff,χ ∼ λ ˜ φ mφ

  • 1. If

meff,χ ∼ mth

χ

  • 2. If

mφ

  • What if ??

mφ

Γ(pert.)

φ

??

meff,χ

∼ g2T2

m2

eff,χ = λ2φ(t)2 + mth χ (T)2

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SLIDE 16

Kyohei Mukaida - Univ. of Tokyo

Introduction

16

Missing Two effects (at least):

➡ Non-perturbative particle production (Preheating) ➡ Thermal dissipation into radiation (via Scatterings)

e.g., [L. Kofman, A. Linde, A. Starobinsky] e.g., [J. Yokoyama; M. Drewes; A. Berera et al.]

meff,χ ∼ λ ˜ φ mφ

  • 1. If

meff,χ ∼ mth

χ

  • 2. If

mφ

m2

eff,χ = λ2φ(t)2 + mth χ (T)2 ∼ g2T2

  • What if ??

mφ

Γ(pert.)

φ

??

meff,χ

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Kyohei Mukaida - Univ. of Tokyo

Main Message

17

Possible sketch of reheating after inflation w/

End of inflation.

Reheating can be completed by

Thermal Dissipation!

Time

Dissipation (Scat.) into high T plasma

mφ ⌧ λφi.

(mφ ⌧ λφi)

Preheating TR High T plasma; is produced and the

preheating terminates: k∗ ∼ mth

χ .

mφ n T

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Kyohei Mukaida - Univ. of Tokyo

Outline

Introduction Preheating (Non-perturb. production) Dissipation to Thermal Plasma Numerical Results

18

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Preheating

19

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Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production

20

The non-perturbative particle production occurs if

Φ’s amplitude: ˜

φ

λ ˜ φ max      mφ, mth

χ (T)2

mφ      

[L. Kofman, A. Linde, A. Starobinsky]

∼ g2T2

ωχ = q k2 + mth

χ (T)2 + λ2φ2(t)

χ

φ

  • vac. fluc.
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Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production

21

The non-perturbative particle production occurs if

Φ’s amplitude: ˜

φ

λ ˜ φ max      mφ, mth

χ (T)2

mφ      

[L. Kofman, A. Linde, A. Starobinsky]

∼ g2T2

ωχ = q k2 + mth

χ (T)2 + λ2φ2(t)

χ

φ

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Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production

22

The non-perturbative particle production occurs if

  • Implies that the non-pert. production is “blocked” if

Φ’s amplitude: ˜

φ

λ ˜ φ max      mφ, mth

χ (T)2

mφ      

[KM, K. Nakayama; K. Enqvist, D. Figueroa, R. Lerner] [L. Kofman, A. Linde, A. Starobinsky]

mth

χ (T) ∼ k∗ =

q λmφ ˜ φ.

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Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production

If χ is not stable, then... Non-perterbatively produced χ can decay within each crossings of Φ~0.

23

  • χ decays completely before the Φ moves back to

its origin if

  • Parametric Resonance is absent in this case;

even if χ is boson. e.g.,[J. Garcia-Bellido, D. Figueroa, J. Rubio]

κ2λ ˜ φ mφ. Γχ ∼ κ2mχ(φ(t)) ∼ κ2λ|φ(t)|;

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Kyohei Mukaida - Univ. of Tokyo

Non-pert. Production

If χ is not stable, then... Non-perterbatively produced χ can decay within each crossings of Φ~0.

24

  • χ decays completely before the Φ moves back to

its origin if

κ2λ ˜ φ mφ.

e.g.,[J. Garcia-Bellido, D. Figueroa, J. Rubio]

  • This process ends @

[λmφ ˜ φ]1/2 ∼ k∗ ∼ mth

χ (T) ∼ gT.

[KM, K. Nakayama]

Γφ ∼ Nd.o.f. λ2mφ 2π4|κ|.

Γχ ∼ κ2mχ(φ(t)) ∼ κ2λ|φ(t)|;

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Thermal Effects

25

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Kyohei Mukaida - Univ. of Tokyo

Thermal Effects

26

  • Thermal Dissipation (Scattering):

¨ φ + (3H + Γφ) ˙ φ + mφ

2φ = −∂F

∂φ

Friction coefficient from Kubo-formula:

  • Small Φ:
  • Large Φ:

[D. Bodeker; M. Laine]

⇒ scatterings including χ.

λφ ⌧ T

⇣ Γφ ∼ λ4φ2/(αT) ⌘ ⇒ scatterings by gauge bosons.

λφ T

… …

Γφ ∼ λ2αT

Γφ ' lim

ω!0

ΠJ(ω, 0) 2ω . φ φ χ χ Aµ Aµ Aµ Aµ e.g.,[Hosoya, Sakagami; J. Yokoyama; M. Drewes]

Γφ ∼ α2 T3 φ2

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Kyohei Mukaida - Univ. of Tokyo

Thermal Effects

27

Typically, there are two effects from thermal plasma.

  • Thermal Dissipation (Scattering):

¨ φ + (3H + Γφ) ˙ φ + mφ

2φ = −∂F

∂φ

Friction coefficient from Kubo-formula:

  • Small Φ:
  • Large Φ:

[D. Bodeker; M. Laine]

⇒ scatterings including χ.

λφ ⌧ T

⇣ Γφ ∼ λ4φ2/(αT) ⌘ ⇒ scatterings by gauge bosons.

λφ T

… …

Γφ ∼ λ2αT

Γφ ' lim

ω!0

ΠJ(ω, 0) 2ω .

  • For mΦ << gT, the inflaton loses its energy by the

thermal dissipation (multiple scattering); not by the perturbative decay!

φ φ χ χ Aµ Aµ Aµ Aµ

Γφ ∼ α2 T3 φ2

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Brief Summary

28

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SLIDE 29

Kyohei Mukaida - Univ. of Tokyo

Reheating after Inflation

29

Rough sketch of reheating after inflation w/

End of inflation. Time

mφ ⌧ λφi.

(mφ ⌧ λφi)

φ

: Inflaton

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SLIDE 30

Kyohei Mukaida - Univ. of Tokyo

Reheating after Inflation

30

Rough sketch of reheating after inflation w/

End of inflation. Time

mφ ⌧ λφi.

(mφ ⌧ λφi)

φ

: Inflaton χ χ χ Decay

Preheating

Radiation χ0, χ00 · · · Aµ

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SLIDE 31

Kyohei Mukaida - Univ. of Tokyo

Reheating after Inflation

31

Rough sketch of reheating after inflation w/

End of inflation. Time

mφ ⌧ λφi.

(mφ ⌧ λφi)

φ

: Inflaton

Radiation

High T plasma; is produced and the

preheating terminates: χ χ χ

χ0, χ00 · · · Aµ

Interaction k∗ ∼ mth

χ .

Preheating

mφ n T

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SLIDE 32

Kyohei Mukaida - Univ. of Tokyo

Reheating after Inflation

32

Rough sketch of reheating after inflation w/

End of inflation. Time

mφ ⌧ λφi.

(mφ ⌧ λφi)

φ

: Inflaton

Radiation

High T plasma; is produced and the

preheating terminates: χ χ χ

χ0, χ00 · · · Aµ

Interaction k∗ ∼ mth

χ .

Preheating

mφ n T Dissipation!

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SLIDE 33

Kyohei Mukaida - Univ. of Tokyo

Reheating after Inflation

33

Rough sketch of reheating after inflation w/

End of inflation.

Reheating can be completed by

Thermal Dissipation!

Time

Dissipation (Scat.) into high T plasma

mφ ⌧ λφi.

(mφ ⌧ λφi)

Preheating TR High T plasma; is produced and the

preheating terminates: k∗ ∼ mth

χ .

mφ n T

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SLIDE 34

Numerical Results

34

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SLIDE 35

Kyohei Mukaida - Univ. of Tokyo

Numerical Results

Reheating via thermal dissipation.

35

Reheating via

Time

TR ∼ 105 GeV

Preheating Dissipation

Γeff

φ ∼ λ2αT

mφ = 1 TeV φi = 1018 GeV λ = 10−5 α = 0.05

“Dissipation”

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SLIDE 36

Kyohei Mukaida - Univ. of Tokyo

Numerical Results

Contour plot of TR as a function of λ and mΦ.

36

TR ∝ q λ2Mplmφ TR ∝ λ2Mpl

“Standard”

TR ∝ q λMplmφ

φi = 1018 GeV α = 0.05

“Dissipation” “Dissipation”

Coupling btw Φ & radiation

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SLIDE 37

Kyohei Mukaida - Univ. of Tokyo

Coupling btw Φ & radiation

Numerical Results

Contour plot of TR as a function of λ and mΦ.

37

TR ∝ q λ2Mplmφ TR ∝ λ2Mpl

“Standard”

TR ∝ q λMplmφ

φi = 1018 GeV α = 0.05

“Dissipation” “Dissipation”

Thermal Dissipation dominates the reheating for small mΦ and not small λ.

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SLIDE 38

Kyohei Mukaida - Univ. of Tokyo

Summary

We studied in detail processes of reheating: particle production from subsequent thermalization and evolution of /plasma system by taking the thermal environment intoaaaaaa If the mass of inflaton is not heavy, TR is dramatically changed due to the thermal dissipation. There are other examples than inflaton.

38

  • particle production from inflaton
  • their subsequent thermalization
  • evolution of inflaton/plasma system

Higgs inflation and its variants; Inflation w/ SUSY flat direction (MSSM inflation); Some class of thermal inflation e.g.,

[T. Moroi, KM, K. Nakayama and T. Takimoto]