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Violent preheating in inflation with nonminimal coupling

Ryusuke Jinno (KEK→IBS)

Based on RJ Ph.D. Thesis

arXiv:1609.05209 w/ Yohei Ema, Kyohei Mukaida and Kazunori Nakayama

Joint KEK Theory Fermilab Theory Meeting @ Fermilab, 26th, Sep., 2016

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Violent preheating in Higgs inflation

Ryusuke Jinno (KEK→IBS)

Based on RJ Ph.D. Thesis

arXiv:1609.05209 w/ Yohei Ema, Kyohei Mukaida and Kazunori Nakayama

Joint KEK Theory Fermilab Theory Meeting @ Fermilab, 26th, Sep., 2016

/ 30

HIGGS DISCOVERY

3

/ 30

HIGGS DISCOVERY

4

/ 30

Inflation : accelerated expansion triggered by “inflaton”

- solves horizon, flatness etc. problems + generates seeds for galaxies

- gives predictions on CMB observation

HIGGS AS THE INFLATON

5

ns

r

/ 30

Inflation : accelerated expansion triggered by “inflaton”

- solves horizon, flatness etc. problems + generates seeds for galaxies

- gives predictions on CMB observation

HIGGS AS THE INFLATON

6

ns

rStarobinsky inflation

Higgs inflation

L ⇠ R+ �2R+ · · ·

L ⇠ R+R2

/ 30

HIGGS AS THE INFLATON

7

Inflaton = Higgs ?

- Nonminimal coupling makes the potential flat

→ Excellent agreement w/ observation

- Sevaral advantages

1. Economical : no need to add new field

2. Predictable : (in principle) the whole history is calculable

[Bezrukov & Shaposhnikov ‘08]

[Cervantes-Cota & Dehnen ‘95]

⇠�2R

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PREHEATING

8

Inflation is only the beginning of the story

Energy transfer from inflaton to light particles

Thermalization of these particles&

t

Inflation

(P)reheating :

BBN, CMB, ...Φ

χ

χ

⇢

[Bezrukov, Gorbunov, Shaposhnikov ’09 Garcia-Bellido, Figueroa, Rubio ’09 and subsequent works]

particles

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Inflation is only the beginning of the story

Energy transfer from inflaton to light particles

Thermalization of these particles&

t

Inflation

(P)reheating :

BBN, CMB, ...Φ

χ

χ

⇢

[Bezrukov, Gorbunov, Shaposhnikov ’09 Garcia-Bellido, Figueroa, Rubio ’09 and subsequent works]

PREHEATINGparticles

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SUMMARY

10

Main channel of energy transfer is overlooked in the literature:

These G.B.s have momentum ~ λ Mp

G.B. energy scale exceeds the cutoff scale → UV completion required

1/2(λ : 4-point coupling of Higgs)

Longitudinal gauge boson

AL AL

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OUTLINE

11

0. Introduction

1. Higgs inflation : Standard lore

2. Higgs inflation : Explosive production of longitudinal G.B.

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Higgs inflation : Standard lore

12

/ 3013

Consider REAL inflaton for the moment, for simplicity

ACTION

Jordan frame :

and are nonminimally coupled ( )�J RJ ⇠�2JR

S =

Zd

4x

p�g

✓M

2P

2+

⇠

2�

2J

◆R� 1

2(@�J)

2 � �

4�

4J

�Real inflaton

Ricci scalar

Free parameter

S =

Zd

4x

p�gJ

✓M

2P

2+

⇠

2�

2J

◆RJ � 1

2(@�J)

2 � VJ(�J)

�

Potential

� ⇠ 0.01

⇠ ⇠ 50000p� � 1

/ 3014

In the absence of coupling ,

this is just chaotic inflation

with potential

↓

observationally excluded

WITHOUT NONMINIMAL COUPLING ...

⇠ ��4J

⇠�2JRJ

�3

�2

�1

ns

r

Φ here4

/ 3015

With coupling , ... Let’s go to the “Einstein frame”

- Conformal transformation

- Ricci scalar transforms as

- Action reduces to ..

WITH NONMINIMAL COUPLING ...

gµ⌫ ⌘ ⌦2gJµ⌫

⇠�2JRJ

S =

Zd

4x

p�g

M

2P

2R+ · · ·

�RJ = ⌦2R+ · · ·

⌦2 = 1 +⇠�2

J

M2P

w/Einstein frame :

No nonminimal coupling

/ 3016

Redefinition of inflaton makes the expression simpler

- Inflaton redef. :

- Potential redef. :

- Action takes the simplest form

INFLATION IN EINSTIEN FRAME

S =

Zd

4x

p�g

M

2P

2R� 1

2(@�)2 � V (�)

�

d�

d�J⌘ 1

⌦2

s

1 +⇠(1 + 6⇠)�2

J

M2P

V (�) ⌘ VJ(�J)

⌦4

⌦2 = 1 +⇠�2

J

M2P

Note : conformal factor

�

V

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Potential in the Einstein frame

17

INFLATION IN EINSTIEN FRAME

�⇠ MP

V (�)

�

[Bezrukov & Shaposhnikov ‘08]

to realize observed scalar perturbation

⇠ ⇠ 50000p� � 1

Note :

Inflation ends

Inflaton oscillates with~ quadratic potential

Inflation

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Let’s make inflaton to be SM Higgs

Taking unitary gauge ( : real ) ,

18

(P)REHEATING

Terms in SM Lagrangian (Gauge boson etc.)

S =

Zd

4x

p�gJ

✓M

2P

2+ ⇠|�J |2

◆RJ � |D�J |2 � VJ(|�J |) + · · ·

�

�J =1p2(0,�J)

T �J

�J

�J

- dynamics : same as real inflaton ( slow-roll → oscillation )

- gauge boson mass oscillates as the inflaton oscillates

8>>>>>>>><>>>>>>>>:

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Note : WRONG argument below !

Gauge boson (3 dof) mass oscillates like

19

(P)REHEATING

- Mass oscillation leads to particle production

- Production of gauge bosons → soon decay into fermions

m2W ⇠ g2�2

J ⇠ g2MP

⇠�m2

AT⇠ g2�2

J ⇠ g2MP

⇠|�| ⇠ | sinmEt|

1

�⇠ MP

V (�)

�

⇠ m2E�

2

(for first ~ 100 oscillations)

- Parametric resonance of gauge bosons (after first ~ 100 oscillations) ... etc.

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Higgs inflation : Explosive gauge boson production

20

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Let’s take U(1) (not SU(2)) gauged Higgs for simplicity

What’s missing in the literature is ...

21

WHAT’S MISSINGIN THE LITERATURE

Mass splitting btw. transverse & longitudinal gauge bosons

m2AT

⇠ g2�2J ⇠ g2

MP

⇠|�|

Note : Both are the same if inflaton is stationary

m2AL

⇠ m2AT

� mAT

mAT

[Lozanov & Amin ‘16]

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Gauge boson action (after taking unitary gauge )

22

MASS SPLITTING OF GAUGE BOSON

�J = �J/p2

m2A =

a2g2�2J

⌦2⌧ : conformal timeNote : ,

SAT =1

2

Zd⌧d3k

(2⇡)3

h| ~A0

T |2 � (k2 +m2A)| ~AT |2

i

SAL =1

2

Zd⌧d3k

(2⇡)3

m2

A

k2 +m2A

|A0L|2 �m2

A|AL|2�

→ mass of the canonical field mass of AT6=AL ⌘r

mA

k2 +m2A

AL

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Longitudinal gauge boson mass has “spike”

23

BEHAVIOR OF LONGITUDINAL MASS

Note : Planck unit Mp = 1 / λ = 0.01 / ξ = 10000

Note :

m2AT

⇠ g2�2J ⇠ g2

MP

⇠|�|

m2AL

⇠ m2AT

� mAT

mAT

�

tt

⇠ m2AL

⇠ (�1/2MP )2

�tspike ⇠ 1/(�1/2MP )

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Origin of the spike

- It contains , and this shows singular behavior why?

- Einstein frame inflaton is oscillating

with ~ quad. potential

- But the map btw. and suddenly changes around the origin

→ next slide

24

BEHAVIOR OF LONGITUDINAL MASS

�J

�J

�

�

Note :

m2AT

⇠ g2�2J ⇠ g2

MP

⇠|�|

m2AL

⇠ m2AT

� mAT

mAT

�

V

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Map btw. two inflatons (note, log scale plot)

25

�

�J

� ⇠ �J

oscillation

� ⇠ log(

p⇠�J/MP )

� ⇠ ⇠�2J/MP

inflation

~ sin(mEt)Einstein

Jordan

BEHAVIOR OF LONGITUDINAL MASS

Map suddenly changes � . MP /⇠for

/ 30

“Spike” correponds to the timescale

with which the inflaton passes

26

BEHAVIOR OF LONGITUDINAL MASS

� . MP /⇠

�tspike ⇠MP /⇠

�⇠ 1

�1/2MP

t

�tspike ⇠ 1/(�1/2MP )

⇠ m2AL

AL AL

/ 30

Backreaction neglected below

Energy of longitudinal G.B.

exceeds inflaton energy

after only one spike

27

LONGITUDINALG.B. PRODUCTION

Longitudinal G.B. energy densityper each log k

Inflaton energy density

wavenumberspike timescale-1

⇠ �1/2MP

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Backreaction must be taken into account, in principle

However, the following statement seems unchanged

“most of the inflaton energy goes into longitudinal G.B.”

though G.B. prod. will cease at some point before exceeding

the inflaton energy

28

BACKREACTION ?

/ 30

Longitudinal G.B. energy exceeds the cutoff scale

29

UNITARITY VIOLATION

Note :

Given by the coefficient of

scalar graviton coupling

Note :

Same in Jordan & Einstein

Longitudinal G.B. produced while crosses this region

�J

p⇠�J

⇠�2J/MP

~ λ Mp1/2

Energy scale of

longitudinal G.B.

�J

[Bezrukov et al. ‘11]

2

/ 30

SUMMARY

30

In Higgs inflation, the main channel of energy transfer is into

through the “mass spike”

These G.B.s have momentum ~ λ Mp

G.B. energy exceeds the cutoff scale

1/2(λ : 4-point coupling of Higgs)

Longitudinal gauge boson

AL AL

/ 3031

Backup

/ 30

BEHAVIOR OF JORDAN INFLATON

32

MP /⇠1/2

p�M2

P /⇠

/ 30

GAUGE BOSON MASSES

33