JPS annual meeting, 14-17 Mar 2019 @ Kyushu Univ.

Oscillons after inflation andgravitational waves

Takashi Hiramatsu
ICRR, The University of Tokyo

Collaboration withEvangelos Sfakianakis (Leiden), Masahide Yamaguchi (TiTech)Inflation models

Takashi Hiramatsu

α-attractor modelattractor model

Planck Collaboration, A&A 594 (2016) A13

Looks good.
But, what if the reheating phase is taken into account ?

Oscillons after inflation and gravitational waves

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Oscillon
α-attractor modelattractor model

Takashi Hiramatsu

Oscillons(= soliton of inflaton)
form due to instability

More gentle potential
than harmonics

Inflaton tends to havelarge field values
Oscillons after inflation and gravitational waves

Pioneer works :Bogolyubosky, Makhankov, PZETF 24 (1976) 15
Gleiser, PRD 49 (1994) 2978
Copeland, Gleiser, Muller, PRD 52 (1995) 1920

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Oscillon

Takashi Hiramatsu

Once oscillons form,
they modify cosmic expansion
history after inflation ?

Physical properties, e.g. life-attractor modeltime,
decaying mechanism, depend on
the shape of inflaton potential.

Oscillons after inflation and gravitational waves

Modify the predictions ?

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GoalTakashi Hiramatsu

As the first step,-attractor model Inflaton potential shapeoscillon formation efficiency-attractor model GWs reveal the existence of oscillons,(is it possible to reconstruct the inflaton potential ?)Related works :Analytic estimation of oscillon decay
Ibe, Kawasaki, Nakano, Sonomoto, arXiv:1901.06130

GWs from oscillons with axion potential
Kitajima, Soda, Urakawa, JCAP (2018) 008

Oscillons after inflation and gravitational waves

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EquationsTakashi Hiramatsu

Field equations+ trace parts

Backreaction to cosmic expansion

slow-attractor modelroll inflation → early matter-attractor modeldominant Universe(we start the simulations atOscillons after inflation and gravitational waves, though)
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Numerical setup

Takashi Hiramatsu

Box size :(comoving)

Grid size :Typical scale of scalar field :Background amplitude :Initial fluctuation :Simulation time :Oscillons after inflation and gravitational waves

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Gravitational waves

Takashi Hiramatsu

Energy spectrum

Observed frequencyOscillons after inflation and gravitational waves

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Past studies

Takashi Hiramatsu

Zhou et al., JHEP 1310 (2013) 026

Antusch, Cefala, Orani, PRL 118 (2017) 011303

Liu et al., PRL 120 (2018) 031301

Kawasaki, Takahashi, Takeda, PRD 92 (2015) 105024

Oscillons after inflation and gravitational waves

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Potential

Takashi Hiramatsu

Zhou et al., JHEP 1310 (2013) 026

Oscillons after inflation and gravitational waves

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Study : small or large

Takashi Hiramatsu

Oscillons can form if the potential
is shallower thanKawasaki, Takahashi, Takeda, PRD 92 (2015) 105024

Oscillons after inflation and gravitational waves

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Study : small or large

Takashi Hiramatsu

Looks similar … ?
Oscillons after inflation and gravitational waves

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Study : small or large

Oscillons after inflation and gravitational waves

Takashi Hiramatsu

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Potential collections

Takashi Hiramatsu

V3
2
2VoutV

1/2
A 1/2

22

1

1

V11

2

12VinV4

Oscillons after inflation and gravitational waves

21V2

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Potential collectionsTakashi Hiramatsu

V322

VoutV1/2
A 1/22211V11212VinV4

Oscillons after inflation and gravitational waves

21V2with

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Results : Potential 1

Takashi Hiramatsu

Inflaton potential

GW : Insensitive
Number : Insensitive
Size : not so changed,
but more broadly
distributed
GW spectrum(note :
(note :
Oscillons after inflation and gravitational waves

Number density

Size distribution))
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Results : Potential 2

Takashi Hiramatsu

Inflaton potential

GW : weak dependence
on small scales
Number : similar evolution,
but weak dependence
Size : typical size is
weakly sensitive tothe height

GW spectrum

Oscillons after inflation and gravitational waves

Number density

Size distribution

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Results : Potential 4

Takashi Hiramatsu

Inflaton potential

GW : insensitive
Number : increasing forshallower potential
Size : not so changed

GW spectrum

Oscillons after inflation and gravitational waves

Number density

Size distribution

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Results : Potential 3
Inflaton potential

Takashi Hiramatsu

GW spectrum

GW : sensitive to the shapeat small field
Number density

Size : fragmentation if thepotential is sharper.
Oscillons after inflation and gravitational waves

Size distribution

Number :-attractor model violent formation atearlier time andquick decay for sharp
potential.
-attractor model mild formation andquick decay for potential
with large power→ non-attractor modelconservation of adiabatic invariant
Ibe, Kawasaki, Nakano, Sonomoto, arXiv:1901.06130
Kawasaki, Takahashi, Takeda, PRD 92 (2015) 105024

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To-do : Instability bands

Takashi Hiramatsu

Linear analysis (Mathieu equation)

Instability bands

Oscillon’s size and shape

Simply spherical→ only a few modes
are unstable

Fragmentated→ many modes areunstable
Oscillons after inflation and gravitational waves

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Summary

Takashi Hiramatsu-attractor model Oscillons in reheating are unwelcome ?

-attractor model Study the oscillon formation and associating
GW spectra with various potentials.

-attractor model Oscillon's life highly depends on small-attractor modelfieldfeature in the potential→ influences GW spectra→ implication : possible to reconstruct ?
Oscillons after inflation and gravitational waves

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