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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
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HIGGS DISCOVERY
3
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HIGGS DISCOVERY
4
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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
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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
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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
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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
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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
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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
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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
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“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
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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 ?
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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
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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
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Backup
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BEHAVIOR OF JORDAN INFLATON
32
MP /⇠1/2
p�M2
P /⇠
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GAUGE BOSON MASSES
33
