Gravitational waves from first-order phase transitions: Towards - - PowerPoint PPT Presentation

Based on 1905.00899 with Hyeonseok Seong (IBS & KAIST), Masahiro Takimoto (Weizmann), Choong Min Um (KAIST) 2019/5/11 @ NHWG 25th regular meeting

Gravitational waves from first-order phase transitions: Towards understanding ultra-supercooled transitions

01 / 19

Ryusuke Jinno (DESY)

Introduction

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ERA OF GRAVITATIONAL WAVES

[LIGO]

Detection of GWs from BH & NS binaries → GW astronomy has started

• Black hole binary 36M⊙ + 29M⊙ →62M⊙
• Frequency ~ 35 to 250 Hz
• Significance > 5.1σ

02

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ERA OF GRAVITATIONAL WAVES

Next will be GW cosmology with space interferometers

重力波天文学のロードマップ

原始重力波シンポ 日本物理学会 年秋季大会 年 月 日 佐賀大学

2010 2015 2020 2025

~10 event/yr のイベントレート

地上望遠鏡

KAGRA Ａｄ. ＬＩＧＯ

LIGO TAMA Enhanced LIGO CLIO Advanced LIGO KAGRA Advanced Virgo VIRGO GEO ET

より遠くを観測 (10Hz-1kHz)

宇宙望遠鏡

0.1mHz-10mHz 確実な重力波源 0.1Hz帯 宇宙論的な重力波

低周波数帯の観測 (1Hz以下)

LPF DECIGO

DECIGO

LISA

BBO LPF DPF Pre- DECIGO LISA

Ground Space

From Ando-san’s talk @ JPS meeting 2014

Taiji, TianQin &

02

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ERA OF GRAVITATIONAL WAVES

Sensitivity curves for current & future experiments

Pulsar timing arrays Space Ground 0.01-1Hz 10 Hz

2

10 Hz

• 8

[http://rhcole.com/apps/GWplotter/]

SOGRO Taiji, TianQin

02

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

SOURCES FOR COSMOLOGICAL GWS

Inflationary quantum fluctuations (“primordial GWs”) Preheating (particle production just after inflation) Topological defects : e.g. cosmic strings, domain walls First-order phase transition often occurs when a symmetry breaks:

03

• Electroweak sym. breaking
• Breaking of GUT group
• PQ sym. breaking
• Strong dynamics

(w/ extension)

• B-L breaking

...

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

First-order phase transition often occurs when a symmetry breaks:

SOURCES FOR COSMOLOGICAL GWS

Inflationary quantum fluctuations (“primordial GWs”) Preheating (particle production just after inflation)

03

• Electroweak sym. breaking
• Breaking of GUT group
• PQ sym. breaking
• Strong dynamics

(w/ extension)

• B-L breaking

...

Topological defects : e.g. cosmic strings, domain walls

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION

false x3 (“nucleation”) true true true Quantum tunneling Field space Bubble formation & GW production false vacuum true vacuum Φ V released energy Position space

How first-order phase transition produces GWs

04

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION

How first-order phase transition produces GWs

false vacuum true vacuum Φ V released energy Bubbles source GWs true true true

GWs ⇤hij ∼ Tij

Field space Position space Bubble formation & GW production Quantum tunneling

04

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

TALK PLAN

• 0. Introduction
• 1. GW production in ultra-supercooled transitions
• 3. Summary
• 2. Effective theory of shock propagation

✔

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

the released energy accumulates on the wall

BEHAVIOR OF BUBBLES

Transition in vacuum

05

• As bubbles expand to "cosmological scale",

zero-temperature eff. potential

true false

∼ ∼

m−1γ−1 m−1 r φ

∼ ∼

m

• Bubbles nucleate with "particle scale" m−1
• Resulting factor can be huge:

γ

cosmological scale

ρreleased

( : typical mass scale of the potential, say, TeV) m

• Bubble surfaces = "walls"

(= where the scalar field value changes)

• r more at the time of collision

∼ 1010 γ

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

true scalar+plasma dynamics

wall

pressure friction false

BEHAVIOR OF BUBBLES

06

thermal potential

ρreleased

Transition in thermal environment

• Two main players : scalar field and plasma

cosmological scale

• Walls want to expand (“pressure”)

m−1 r φ

∼ ∼

m−1

• Walls are pushed back by plasma (“friction”)

Controlled by α ≡ ρreleased

ρplasma

Controlled by coupling btwn. scalar and plasma

η α

• Let's see how bubbles behave for different

η

(with fixed )

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

BUBBLE EXPANSION IN THERMAL TRANSITION

07

0.0 0.2 0.4 0.6 0.8 1.0 r / t 0.1 0.2 0.3 0.4 0.5 vfluid 0.0 0.2 0.4 0.6 0.8 1.0 r / t 0.6 0.8 1.0 1.2 T / T∞ Temperature

Fluid outward velocity

wall position wall position “deflagration”

Small

α (. O(0.1)) α ≡ ρreleased ρplasma

[ Espinosa, Konstandin, No, Servant ’10 ]

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks" 07

Temperature

0.0 0.2 0.4 0.6 0.8 1.0 r / t 0.9 1.0 1.1 1.2 1.3 T / T∞ 0.0 0.2 0.4 0.6 0.8 1.0 r / t 0.1 0.2 0.3 0.4 vfluid

wall position wall position

α ≡ ρreleased ρplasma

Fluid outward velocity

“detonation”

[ Espinosa, Konstandin, No, Servant ’10 ]

Small but slightly increased α (. O(0.1))

BUBBLE EXPANSION IN THERMAL TRANSITION

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks" 07

Temperature

wall position

0.0 0.2 0.4 0.6 0.8 1.0 r / t 1 2 3 4 5 T / T∞

wall position

0.0 0.2 0.4 0.6 0.8 1.0 r / t 2 4 6 8 10 12 14 γfluid

Large

α ( 1) α ≡ ρreleased ρplasma

Fluid outward velocity

“strong detonation”

[ Espinosa, Konstandin, No, Servant ’10 ]

BUBBLE EXPANSION IN THERMAL TRANSITION

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

KNOWNS AND UNKNOWNS

The system BEFORE bubble collisions is relatively known

08

Less known is the system AFTER collisions

• Nucleation rate is calculable from the potential

(note but : gauge-dependence is an issue when the scalar field is gauged)

• Behavior of fluid (i.e. coarse-grained plasma) is calculable from

∂µT µν

fluid = 0

with an energy-injection boundary condition at the wall position

• This is important to predict GWs = observable

[ e.g. Chiang & Senaha '17 ]

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

KNOWNS AND UNKNOWNS

The system BEFORE bubble collisions is relatively known

08

Less known is the system AFTER collisions

• Nucleation rate is calculable from the potential

(note but : gauge-dependence is an issue when the scalar field is gauged)

• Behavior of fluid (i.e. coarse-grained plasma) is calculable from

∂µT µν

fluid = 0

with an energy-injection boundary condition at the wall position

• This is important to predict GWs = observable

[ e.g. Chiang & Senaha '17 ]

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

DYNAMICS AFTER COLLISION

Bubbles nucleate & expand

09

• Typically collide after expansion

∆t ∼ 1/β

• Nucleation rate (per unit time & vol)

Γ(t) ∝ eβt

1/β : some const.

with

• Released energy is

[ Bodeker & Moore ’17 ]

mainly carried by fluid motion

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

DYNAMICS AFTER COLLISION

Bubbles nucleate & expand

• Typically collide after expansion

∆t ∼ 1/β

• Nucleation rate (per unit time & vol)

Γ(t) ∝ eβt

1/β : some const.

with

09

• Released energy is

[ Bodeker & Moore ’17 ]

mainly carried by fluid motion

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

DYNAMICS AFTER COLLISION

Bubbles collide

• Scalar field damps soon after collision

Ryusuke Jinno

GWs ⇤hij ∼ Tij

“sound waves”

• For small , plasma motion is

α

well described by linear approximation:

(. O(0.1))

(∂2

t − c2 s ∇2)

⃗ v ≃ 0

• In this case, fluid shell thickness is

fixed at the time of collision

• Dynamics for is almost unknown

α ( 1)

09

1605.01403 / 1707.03111 / 1708.01253

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

DYNAMICS AFTER COLLISION

Turbulence develops

• Nonlinear effects are believed to appear

“turbulence”

GWs ⇤hij ∼ Tij

at sufficiently late times

• However, no numerical simulations

09

have confirmed this (even for )

α(. O(0.1))

starting from the beginning of the transition

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

What we do when we predict GWs from particle physics models:

Particle physics model Prediction on GWs Parameters relevant to phase transition

10

• Released energy (i.e. )
• Nucleation rate (i.e. )
• Transition temperature ... and so on

α

β

L

→ We would like to develop an alternative approach

• To prepare for future observations, we have to understand well
• Currently, understanding on is mainly driven by numerical simulations

ρGW

e.g. CMB, Lattice QCD, ...

• However, numerical approach alone does not give good understanding of the system

AIM OF OUR PROJECT(S): ANALYTIC (NON-NUMERICAL) UNDERSTANDING

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ULTRA-SUPERCOOLED TRANSITION

In some models, is realized

11

But numerical simulation is almost impossible due to

α ≡ ρreleased ρplasma ≫ 1

• How? e.g. classically conformal setups:

∼ λ(ϕ)ϕ4

Zero-temerature: Coleman-Weinberg potential

∝ T2ϕ2

Thermal trap: persists Energy release

1) Hierarchy in scales: fluid shell thickness << bubble radius << simulation box 2) Strong shock waves (discontinuity) in the fluid front

These models are also observationally motivated because □ hij ∼ Tij

big big

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ULTRA-SUPERCOOLED TRANSITION

In some models, is realized

11

But numerical simulation is almost impossible due to

α ≡ ρreleased ρplasma ≫ 1

• How? e.g. classically conformal setups:

∼ λ(ϕ)ϕ4

Zero-temerature: Coleman-Weinberg potential

∝ T2ϕ2

Thermal trap: persists Energy release

1) Hierarchy in scales: fluid shell thickness << bubble radius << simulation box 2) Strong shock waves (discontinuity) in the fluid front

These models are also observationally motivated because □ hij ∼ Tij

big big

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ULTRA-SUPERCOOLED TRANSITION

In some models, is realized

11

But numerical simulation is almost impossible due to

α ≡ ρreleased ρplasma ≫ 1

[ イメージ ]

Huge energy release Relativistic fluid

These models are also observationally motivated because

∼ λ(ϕ)ϕ4

Zero-temerature: Coleman-Weinberg potential

∝ T2ϕ2

Thermal trap: persists Energy release

1) Hierarchy in scales: fluid shell thickness << bubble radius << simulation box 2) Strong shock waves (discontinuity) in the fluid front □ hij ∼ Tij

big big

• How? e.g. classically conformal setups:

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

These models are also observationally motivated because □ hij ∼ Tij

big big

ULTRA-SUPERCOOLED TRANSITION

In some models, is realized

11

But numerical simulation is almost impossible due to

α ≡ ρreleased ρplasma ≫ 1

[ イメージ ]

Huge energy release Relativistic fluid

∼ λ(ϕ)ϕ4

Zero-temerature: Coleman-Weinberg potential

∝ T2ϕ2

Thermal trap: persists Energy release

1) Hierarchy in scales: fluid shell thickness << bubble radius << simulation box 2) Strong shock waves (discontinuity) in the fluid front Here

• How? e.g. classically conformal setups:

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

ULTRA-SUPERCOOLED TRANSITION

Then, how do people usually predict the final GW spectrum?

12

We have to understand the dynamics of ultra-supercooled system. But how?

• They (ab)use simulation results (i.e. linear system )

α ≲ 𝒫(0.1) (∂2

t − c2 s ∇2)

⃗ v ≃ 0 Fluid overlapping effect boosts the GW spectrum by in the linear system 𝒫(102−5) Tij ∼ (ρ + p)vivj

linear linear nonlinear

[ Hindmarsh '17 ]

• However, no guarantee that this applies to ultra-supercooled case (i.e. relativistic )

⃗ v Note

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

TALK PLAN

• 0. Introduction
• 1. GW production in ultra-supercooled transitions
• 3. Summary
• 2. Effective theory of shock propagation

✔ ✔

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

REDUCING THE PROBLEM

Let's devide the problem into small pieces:

13

Even propagation is nontrivial due to nonlinearity in fluid equation. 1) propagation of relativistic fluid This time we work on propagation only. 2) collision of relativistic fluid

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

STRATEGY

14

Our strategy: 1) Develop an effective theory of fluid propagation which is valid in high-relativisticity regime 2) Compare the theory with (small, fluid-propagation only) simulation in mildly-relativistic regime

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

EFFECTIVE THEORY OF FLUID PROPAGATION

14

Before constructing a theory, let's see numerical simulation (in 1+1 dim.)

• Perfect fluid & relativistic EoS

Tμν = (ρ + p)uμuν − pημν p = ρ/3

fluid energy density relativistic factor squared

γ

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

EFFECTIVE THEORY OF FLUID PROPAGATION

14

Before constructing a theory, let's see numerical simulation (in 1+1 dim.)

• Perfect fluid & relativistic EoS

Tμν = (ρ + p)uμuν − pημν p = ρ/3

fluid energy density relativistic factor squared

γ

• Profile at the collision time (blue) propagates inside true vacuum fluid (others)

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

EFFECTIVE THEORY OF FLUID PROPAGATION

14

Before constructing a theory, let's see numerical simulation (in 1+1 dim.)

• Perfect fluid & relativistic EoS

Tμν = (ρ + p)uμuν − pημν p = ρ/3

fluid energy density relativistic factor squared

γ

• Profile at the collision time (blue) propagates inside true vacuum fluid (others)
• Peaks rearrange to new initial values, and gradually become less energetic

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

EFFECTIVE THEORY OF FLUID PROPAGATION

14

Before constructing a theory, let's see numerical simulation (in 1+1 dim.)

• Perfect fluid & relativistic EoS

Tμν = (ρ + p)uμuν − pημν p = ρ/3

fluid energy density relativistic factor squared

γ

• Profile at the collision time (blue) propagates inside true vacuum fluid (others)
• Strong shocks (i.e. discontinuities) persist during propagation
• Peaks rearrange to new initial values, and gradually become less energetic

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

EFFECTIVE THEORY OF FLUID PROPAGATION

15

Can we construct a theory for fluid propagation?

• From the viewpoint of GW production, we are interested only in PEAKS, not TAILS
• Can we describe the time evolution of peak-related quantities?

vs 1) Shock velocity: 2) Peak values: (equivalently ) ρpeak, vpeak ρpeak, γ2

peak

3) Derivatives at the peak: @ shock front dρpeak dr , dvpeak dr

1 2 3

• We constructed a "closed equation system" for these quantities

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

HOW TO MAKE A CLOSED SYSTEM

16

• Rankine-Hugoniot conditions across the shock : 2 constraints
• Time evolution equations : 2 evolution equations

Closed system for 5 quantities γ2

s , ρpeak, γ2 peak,

dρpeak dr , dγ2

peak

dr (corresponding to energy and momentum conservation across the shock) (corresponding to temporal & spacial part of ) ∂μTμν = 0

• Energy (or momentum) domination by the shock front : 1 condition

(takes a form like ) ρpeakγ2

peak ×

1 dρpeak/dr or dγ2

peak/dr = const .

i.e. peak energy density × typical thickness = const.

approx. relation

1 2 3

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

HOW TO MAKE A CLOSED SYSTEM

16

• Rankine-Hugoniot conditions across the shock : 2 constraints
• Time evolution equations : 2 evolution equations

Closed system for 5 quantities γ2

s , ρpeak, γ2 peak,

dρpeak dr , dγ2

peak

dr (corresponding to energy and momentum conservation across the shock) (corresponding to temporal & spacial part of ) ∂μTμν = 0

• Energy (or momentum) domination by the shock front : 1 condition

(takes a form like ) ρpeakγ2

peak ×

1 dρpeak/dr or dγ2

peak/dr = const .

i.e. peak energy density × typical thickness = const.

approx. relation

1 2 3

(relativistic limit)

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

HOW TO MAKE A CLOSED SYSTEM

16

• Rankine-Hugoniot conditions across the shock : 2 constraints
• Time evolution equations : 2 evolution equations

Closed system for 5 quantities γ2

s , ρpeak, γ2 peak,

dρpeak dr , dγ2

peak

dr (corresponding to energy and momentum conservation across the shock) (corresponding to temporal & spacial part of ) ∂μTμν = 0

• Energy (or momentum) domination by the shock front : 1 condition

(takes a form like ) ρpeakγ2

peak ×

1 dρpeak/dr or dγ2

peak/dr = const .

i.e. peak energy density × typical thickness = const.

approx. relation

1 2 3

f

:

planar cylindical spherical

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

HOW TO MAKE A CLOSED SYSTEM

16

• Rankine-Hugoniot conditions across the shock : 2 constraints
• Time evolution equations : 2 evolution equations

Closed system for 5 quantities γ2

s , ρpeak, γ2 peak,

dρpeak dr , dγ2

peak

dr (corresponding to energy and momentum conservation across the shock) (corresponding to temporal & spacial part of ) ∂μTμν = 0

• Energy (or momentum) domination by the shock front : 1 condition

(takes a form like ) ρpeakγ2

peak ×

1 dρpeak/dr or dγ2

peak/dr = const .

i.e. peak energy density × typical thickness = const.

approx. relation

1 2 3

f

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

THEORY PREDICTION

We can solve the effective system (for )

18

d = 3 δ = 10 13 1) Shock velocity: 2) Peak values: 3) Derivatives at the peak:

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

COMPARISON WITH NUMERICAL SIMULATION

Analytical vs. numerical

(blue: data) γ2

s

ρpeak, γ2

peak

dρpeak dr , dγ2

peak

dr

17

(red: theory)

• Qualitatively OK!

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

IMPLICATIONS TO GW PRODUCTION

Implication: fluid profile remains relativistic & thin until late times

18

• May indicate delay

in the onset of sound waves

• Still not conclusive,

since we neglected collisions

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

IMPLICATIONS TO GW PRODUCTION

Implication: fluid profile remains relativistic & thin until late times

18

• May indicate delay

in the onset of sound waves

• Still not conclusive,

since we neglected collisions Numerical simulation is (barely) possible Effective description is valid Fluid "lifetime" 𝒫(1) (time for fluid to damp to ) normalized by bubble size @ collision

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

IMPLICATIONS TO GW PRODUCTION

Implication: fluid profile remains relativistic & thin until late times

18

• May indicate delay

in the onset of sound waves

• Still not conclusive,

since we neglected collisions 2 years ago I and Masahiro solved thin-wall system completely:

[1707.03111]

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

IMPLICATIONS TO GW PRODUCTION

Implication: fluid profile remains relativistic & thin until late times

18

• May indicate delay

in the onset of sound waves

• Still not conclusive,

since we neglected collisions 2 years ago I and Masahiro solved thin-wall system completely:

[1707.03111]

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

TALK PLAN

• 0. Introduction
• 1. GW production in ultra-supercooled transitions
• 3. Summary
• 2. Effective theory of shock propagation

✔ ✔ ✔

Ryusuke Jinno, / 19

1905.00899 "GWs from first-order phase transitions: Ultra-supercooled transitions and the fate of relativistic shocks"

SUMMARY

19

GW production in ultra-supercooled transitions is interesting both theoretically and observationally, but numerical simulation is almost impossible α ≡ ρreleased ρplasma ≫ 1 We reduced the problem into (1) propagation and (2) collision, and tackled (1) We constructed an effective theory for relativistic fluid propagation, and cross-checked with numerical results in mildly-relativistic regime Using the theory we got implications to GW production, though the study is still halfway through

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