Unemployment and Inflation. Unemployment and Inflation Nature of Unemployment.
Oscillons after inflation and gravitational wavesresonance/pdf_workshop/... · 2019. 5. 16. ·...
Transcript of Oscillons after inflation and gravitational wavesresonance/pdf_workshop/... · 2019. 5. 16. ·...
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 ?