Gravitational waves from bubble dynamics: Beyond the Envelope

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1 Gravitational waves from bubble dynamics: Beyond the Envelope Masahiro Takimoto (WIS, KEK) Based on arxiv: (PRD95, ) & with Ryusuke Jinno (IBS-CTPU) Aug.09, TevPa / 22

2 Introduction

3 ERA OF GRAVITATIONAL WAVES First detection of GWs from BH binaries GW astronomy has started - Black hole binary 36M + 29M 62M - Frequency ~ 35 to 250 Hz - Significance > 5.1σ [LIGO] 03

4 ERA OF GRAVITATIONAL WAVES Detection of GWs from BH binaries GW astronomy has started Next will come GW cosmology with space interferometers e.g. LISA, DECIGO, BBO,... First-order phase transitions can be cosmological GW sources - Electroweak sym. breaking (w/ extensions) - PQ sym. breaking - B-L breaking - GUT breaking... etc. Masahiro Takimoto 04 / 22

5 GRAVITATIONAL WAVES AS A PROBE TO PHASE TRANSITION How (first order) phase transition occurs - High temperature - Low temperature false vacuum true vacuum V V V Φ Trapped at symmetry enhanced point Φ Another extreme appears Φ Another extreme becomes stable Time 05 / 22

6 GWS AS A PROBE TO PHASE TRANSITION Thermal first-order phase transition produces GWs in early universe - Field space - Position space false vacuum true vacuum true V released energy true false true ( nucleation ) Φ x 3 Quantum tunneling Bubble formation & GW production Masahiro Takimoto 06 / 22

7 GWS AS A PROBE TO PHASE TRANSITION Thermal first-order phase transition produces GWs in early universe - Field space - Position space false vacuum true vacuum GWs h T V released energy true true true Bubble walls source GWs Φ Quantum tunneling Bubble formation & GW production Masahiro Takimoto 07 / 22

8 GRAVITATIONAL WAVES AS A PROBE TO PHASE TRANSITION GWs propagates until the present without losing information because of the Planck-suppressed interaction of gravitions GWs propagation Phase transition & GW production NO scattering = NO information loss present t Masahiro Takimoto 08 / 22

9 GRAVITATIONAL WAVES AS A PROBE TO PHASE TRANSITION GWs propagates until the present without losing information GWs can be a unique probe to unknown high-energy particle physics because of the Planck-suppressed interaction of gravitions GWs propagation Phase transition & GW production NO scattering = NO information loss present t Masahiro Takimoto 09 / 22

10 ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION GWs behave as non-interacting radiation after production frequency : f / a 1 (redshift) energy density : GW / a 4 Frequency & energy scale correspondence Present GW frequency Energy scale of the GW production time f 0 1 Hz H T 10 7 GeV H O(101 4 ) Note: Planed space interferometers are sensitive to (sub) Hz GWs. They are sensitive to new physics around TeV-PeV range!! Masahiro Takimoto 10 / 22

11 TALK PLAN 0. Introduction 1. Analytic derivation of the GW spectrum 2. Result 3. Conclusion Masahiro Takimoto 11 / 22

12 1. Analytic derivation of GW spectrum Masahiro Takimoto 12 / 22

13 2. ANALYTIC DERIVATION OF THE GW SPECTRUM The essence : GW spectrum is determined by ht ij (t x, x)t kl (t y, y)i ens ll Ensemble average [Caprini et al. 08] Masahiro Takimoto 13 / 22

14 2. ANALYTIC DERIVATION OF THE GW SPECTRUM The essence : GW spectrum is determined by ht ij (t x, x)t kl (t y, y)i ens - Why Note : indices omitted below Formal solution of EOM : h T h Z t dt 0 Green(t, t 0 )T (t 0 ) Energy density of GWs (~ GW spectrum) : GW (t) hḣ2 i ens 8 G Z t dt x Z t dt y cos(k(t x t y ))htti ens same as massless scalar field substitute the formal solution Note : ensemble average because of the stochasticity of the bubbles Masahiro Takimoto 14 / 22

15 2. ANALYTIC DERIVATION OF THE GW SPECTRUM The essence : GW spectrum is determined by We have to specify energy momentum tensor of the system. In thermal phase transition, following 3 ingredients are important. 1. Space-time distribution of the bubbles (nucleation points). Determined by transition rate 2. Energy momentum profile around bubble. We adopt thin wall approximation. Good for low frequencies. 3. Dynamics after bubble collision. Envelope approximation is often applied. [Kosowsky, Turner, Watkins, PRD45 ( 92)] ht ij (t x, x)t kl (t y, y)i ens Beyond envelope! [Hindmarsh et al. 14] *Late time GW enhancement was suggested. *We did a robust estimate of GW spectrum assuming free propagation! Masahiro Takimoto 15 / 22

16 2. ANALYTIC DERIVATION OF THE GW SPECTRUM Estimate of the ensemble average - Trivial from the definition of ensemble average ht (t x, x)t (t y, y)i ens = B Probability T (t x, x)t (t y, y) 0 (t x, x) (t y, y) 0 ll Probability that bubble walls are passing through (t x, x)&(t y, y) ht (t x, x)t (t y, y)i ens Note: We have fixed behaviour of energy momentum tensor of the system. 0 (P) Probability part (V) Value part Value of T (t x, x)t (t y, y) in that case Masahiro Takimoto 16 / 22 0

17 FULL EXPRESSIONS Full expression reduces to only ~10-dim. integration [Jinno & Takimoto 17] A part of the result. Calculation is tedious but straightforward. Masahiro Takimoto 17 / 22

18 TALK PLAN 0. Introduction 1. Analytic derivation of the GW spectrum 2. Result 3. Conclusion Masahiro Takimoto 18 / 22

19 NUMERICAL RESULT A result Long duration Damping func. D ~ e - t / τ after collision Instant disappearance (envelope) [Jinno&Takimoto 16] coincide with [Huber&Konstandin 08] within factor 2 tau: sourcing time after collision. [Jinno & Takimoto 17] Masahiro Takimoto 19 / 22

20 NUMERICAL RESULT A result Linear ( k) behavior Sourcing saturates for fixed k Sourcing moves to low k [Jinno & Takimoto 17] Masahiro Takimoto 20 / 22

21 NUMERICAL RESULT A result Linear ( k) behavior We confirmed enhancement of GW in low frequencies!! [Jinno & Takimoto 17] Masahiro Takimoto 21 / 22

22 SUMMARY & FUTURE PROSPECTS GW spectrum w/ thin-wall has been derived ANALYTICALLY - General nucleation rate & wall velocity & damping of wall energy We have obtained GW spectrum in lower frequencies. - The huge enhancement compared to the envelope approximation Various effects can be implemented - Cosmic expansion / Nucl. rate dependence / Wall thickness (w/ truncation?) Will deepen our understanding on GW sourcing Masahiro Takimoto 22 / 22

23 Back up

24 GWS AS A PROBE TO PHASE TRANSITION Rough range of GW amplitude ~quadrupole factor ~radiation fraction today 10 7 GW Detector sensitivities :typical bubble at transition GW = GW / tot T : temp. just after transition : H just after transition H Model dependent parameter GW from gravitational waves are sensitive to new physics around TeV-PeV range!! f Hz : elisa : LISA : DECIGO : BBO

25 BEHAVIOR OF SINGLE BUBBLE Two main players : scalar field & plasma pressure scalar+plasma dynamics true wall friction false - Walls (where the scalar field value changes) want to expand ( pressure ) - Walls are pushed back by plasma ( friction ) Bubble (wall & surrounding plasma) behavior is determined by released rad & O(0.1). O(0.1) : Huge energy release : Small energy release

26 BEHAVIOR OF SINGLE BUBBLE Understanding until ~ 2016 [e.g. Bodeker & Moore, JCAP 0905 (2009) 009 Espinosa et al., JCAP 1006 (2010) 028] & O(0.1) : Huge energy release Runaway pressure friction wall : Small energy release. O(0.1) plasma bulk motion pressure friction cs wall - Plasma friction cannot balance with pressure - Walls approach the speed of light - Energy accumulates in walls Terminal velocity (to experts : this is detonation case) - Plasma friction gets balanced with pressure - Walls approach terminal velocity - Energy accumulates in plasma bulk motion

27 BEHAVIOR OF SINGLE BUBBLE Understanding from 2017 ~ & O(0.1) plasma bulk motion pressure pressure : Huge energy release cs wall : Small energy release. O(0.1) plasma bulk motion cs wall friction / w transition splitting friction [Bodeker & Moore 17] Runaway High-terminal velocity - Plasma friction can balance with pressure - Walls approach high terminal velocity - Energy accumulates in plasma bulk motion Low-terminal velocity - Plasma friction gets balanced with pressure - Walls approach terminal velocity - Energy accumulates in plasma bulk motion

28 BEHAVIOR AFTER COLLISION What happens after collisions? 1. Walls (energetically subdominant) collide and damp soon bubble collision 2. Plasma bulk motion continues to propagate sound wave true 3. At late times, sound waves develop into nonlinear regime turbulence

29 BEHAVIOR AFTER COLLISION (thin-wall) What happens after collisions? (envelope) 1. Walls (energetically subdominant) collide and damp soon bubble collision 2. Plasma bulk motion continues to propagate sound wave [Kosowski et al. 93] true 3. At late times, sound waves develop into nonlinear regime turbulence

BEHAVIOR AFTER COLLISION What happens after collisions? 1. Walls (energetically subdominant) collide and damp soon bubble collision [Hindmarsh et al. 15] 2.

30 BEHAVIOR AFTER COLLISION What happens after collisions? 1. Walls (energetically subdominant) collide and damp soon bubble collision [Hindmarsh et al. 15] 2. Plasma bulk motion continues to propagate sound wave true (1) Dynamics is linear for small energy release c2s r2 i u =0 ui : fluid velocity field (2) Width remains to be constant after collision

31 ONLY TWO CASES Following two exhaust T (x)t (y) 6= 0 possibilities [Jinno & Takimoto 16] 1. single-bubble (t x, x) (t y, y) nucleation point 2. double-bubble (t y, y) (t x, x) Masahiro Takimoto

32 PHYSICAL INTERPRETATION Small wavenumbers sourced at late times - Wavenumber k sourced when the typical bubble size grows to ~ 1/k GWs with wavenumber k ~ 1/k 27

33 NUMERICAL RESULT GW sourcing as a function of time - Single - Double

34 WHY SINGLE-BUBBLE MATTERS Illustration with envelope - Two bubble-wall fragments must remain uncollided until they reach x and y - Other parts of the bubble might have collided already - In this sense, breaking of spherical sym. is automatically taken into account

Gravitational waves from phase transitions: an analytic approach

Gravitational waves from phase transitions: an analytic approach Ryusuke Jinno (IBS-CTPU) Based on arxiv:1605.01403 (PRD95, 024009) & 1707.03111 with Masahiro Takimoto (Weizmann Institute) Jan. 8, 2018,