Oscillons after inflation and gravitational waves

ICRR, The University of Tokyo

Takashi Hiramatsu

Evangelos Sfakianakis (Leiden), Masahide Yamaguchi (TiTech)

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

Collaboration with

Oscillons after inflation and gravitational waves 2/21

Takashi HiramatsuInflation models

α-attractor modelattractor model

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

Planck Collaboration, A&A 594 (2016) A13

Oscillons after inflation and gravitational waves 3/21

Takashi HiramatsuOscillon

α-attractor modelattractor model Oscillons

(= soliton of inflaton)

form due to instability

More gentle potential

than harmonics

Inflaton tends to have

large field values Bogolyubosky, Makhankov, PZETF 24 (1976) 15

Gleiser, PRD 49 (1994) 2978

Copeland, Gleiser, Muller, PRD 52 (1995) 1920

Pioneer works :

Oscillons after inflation and gravitational waves 4/21

Takashi HiramatsuOscillon

Physical properties, e.g. life-attractor modeltime,

decaying mechanism, depend on

the shape of inflaton potential.

Once oscillons form,

they modify cosmic expansion

history after inflation ?

Modify the predictions ?

Oscillons after inflation and gravitational waves 5/21

Takashi HiramatsuGoal

-attractor model Inflaton potential shape

As the first step,

Related works :

Analytic estimation of oscillon decayIbe, Kawasaki, Nakano, Sonomoto, arXiv:1901.06130

-attractor model GWs reveal the existence of oscillons, (is it possible to reconstruct the inflaton potential ?)

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

oscillon formation efficiency

Oscillons after inflation and gravitational waves 6/21

Takashi HiramatsuEquations

Field equations

+ trace parts

Backreaction to cosmic expansion

slow-attractor modelroll inflation → early matter-attractor modeldominant Universe

(we start the simulations at , though)

Oscillons after inflation and gravitational waves 7/21

Takashi HiramatsuNumerical setup

Box size :

Grid size :

Initial fluctuation :

Background amplitude :

Typical scale of scalar field :

Simulation time :

(comoving)

Oscillons after inflation and gravitational waves 8/21

Takashi HiramatsuGravitational waves

Energy spectrum

Observed frequency

Oscillons after inflation and gravitational waves 9/21

Takashi HiramatsuPast studies

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 10/21

Takashi HiramatsuPotential

Zhou et al., JHEP 1310 (2013) 026

Oscillons after inflation and gravitational waves 11/21

Takashi HiramatsuStudy : small or large

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

Oscillons can form if the potential

is shallower than

Oscillons after inflation and gravitational waves 12/21

Takashi HiramatsuStudy : small or large

Looks similar … ?

Oscillons after inflation and gravitational waves 13/21

Takashi HiramatsuStudy : small or large

Oscillons after inflation and gravitational waves 14/21

Takashi HiramatsuPotential collections

V1

V3

V2

V4

Vout

Vin

VA

2

2

2

2

2

1

2

1 1

1

1

2

2

1/21/2

Oscillons after inflation and gravitational waves 15/21

Takashi HiramatsuPotential collections

V1

V3

V2

V4

Vout

Vin

VA

2

2

2

2

2

1

2

1 1

1

1

2

2

1/21/2

with

Oscillons after inflation and gravitational waves 16/21

Takashi HiramatsuResults : Potential 1

GW : Insensitive

(note : )

Number : Insensitive

Size : not so changed, but more broadly distributed

GW spectrum Number density Size distribution

Inflaton potential

(note : )

Oscillons after inflation and gravitational waves 17/21

Takashi HiramatsuResults : Potential 2

GW : weak dependence on small scales

Number : similar evolution, but weak dependence

Size : typical size is weakly sensitive to the height

GW spectrum Number density Size distribution

Inflaton potential

Oscillons after inflation and gravitational waves 18/21

Takashi HiramatsuResults : Potential 4

GW : insensitive

Number : increasing for shallower potential

Size : not so changed

GW spectrum Number density Size distribution

Inflaton potential

Oscillons after inflation and gravitational waves 19/21

Takashi HiramatsuResults : Potential 3

→ non-attractor modelconservation of adiabatic invariantIbe, Kawasaki, Nakano, Sonomoto, arXiv:1901.06130Kawasaki, Takahashi, Takeda, PRD 92 (2015) 105024

GW : sensitive to the shape at small field

Number : -attractor model violent formation at earlier time and quick decay for sharp potential. -attractor model mild formation and quick decay for potential with large power

Size : fragmentation if the potential is sharper.

GW spectrum

Number density Size distribution

Inflaton potential

Oscillons after inflation and gravitational waves 20/21

Takashi HiramatsuTo-do : Instability bands

Instability bands Oscillon’s size and shape

Simply spherical→ only a few modes are unstable

Fragmentated→ many modes are unstable

Linear analysis (Mathieu equation)

Oscillons after inflation and gravitational waves 21/21

Takashi HiramatsuSummary

-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 modelfield

feature in the potential

→ influences GW spectra

→ implication : possible to reconstruct ?