Gravitational waves from phase transitions: an analytic approach

Transcription

1 Gravitational waves from phase transitions: an analytic approach Ryusuke Jinno (IBS-CTPU) Based on arxiv: (PRD95, ) & with Masahiro Takimoto (Weizmann Institute) Jan. 8, 2018, High 1 workshop 01 / 22

2 Introduction

3 ERA OF GRAVITATIONAL WAVES Detection of GWs from BH & NS binaries GW astronomy has started [LIGO] - Black hole binary 36M + 29M 62M - Frequency ~ 35 to 250 Hz - Significance > 5.1σ Ryusuke Jinno 02 / 22

4 ERA OF GRAVITATIONAL WAVES Next will be GW cosmology with space interferometers 地上望遠鏡 Ground より遠くを観測 (10Hz-1kHz) 宇宙望遠鏡 Space 低周波数帯の観測 (1Hz 以下 ) 2010 LIGO Enhanced LIGO Advanced LIGO TAMA KAGRA CLIO VIRGO GEO Advanced Virgo LPF LPF DPF 2015 Ad. LIGO KAGRA ET LISA LISA Pre- DECIGO 2020 ~10 event/yr のイベントレート 0.1mHz-10mHz 確実な重力波源 BBO Taiji DECIGO Hz 帯宇宙論的な重力波 DECIGO From Ando-san s JPS meeting 2014 Ryusuke Jinno 02 / 22

5 ERA OF GRAVITATIONAL WAVES Sensitivity curves for current & future experiments Pulsar timing arrays Space Ground 10-8Hz Hz 102 Hz [ Ryusuke Jinno 02 / 22

6 ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION How thermal first-order phase transition produces GWs Field space Position space false vacuum true vacuum true V Φ released energy true false true ( nucleation ) x 3 Quantum tunneling Bubble formation & GW production Ryusuke Jinno 03 / 22

7 ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION How thermal first-order phase transition produces GWs Field space Position space false vacuum true vacuum GWs h ij T ij V released energy true true true Bubbles source GWs Φ Quantum tunneling Bubble formation & GW production Ryusuke Jinno 03 / 22

8 ROUGH SKETCH OF PHASE TRANSITION & GW PRODUCTION GWs just redshift as non-interacting radiation after production Transition time Redshift : frequency energy f / a 1 GW / a 4 t Frequency & energy scale correspondence t = t 0 f 0 1 Hz H T 10 7 GeV H O(101 4 ) f 0 : Present GW frequency T : Temperature of the transition time Hz detectors sensitive to EW, TeV, PeV physics Ryusuke Jinno 04 / 22

9 TALK PLAN 0. Introduction 1. Bubble dynamics in first-order phase transitions 2. Analytic approach to GW production 3. Future prospects Ryusuke Jinno / 22

10 BEHAVIOR OF BUBBLES Two main players : scalar field & plasma [e.g. Espinosa et al., JCAP06(2010)028] pressure scalar+plasma dynamics true friction false wall - Walls (where the scalar field value changes) want to expand ( pressure ) - Walls are pushed back by plasma ( friction ) Walls make thermal plasma motion : Case 1 v w & 1/ p 3 (Detonation) plasma bulk motion true v w false v w Ryusuke Jinno 05 / 22

11 BEHAVIOR OF BUBBLES Two main players : scalar field & plasma [e.g. Espinosa et al., JCAP06(2010)028] pressure scalar+plasma dynamics true friction false wall - Walls (where the scalar field value changes) want to expand ( pressure ) - Walls are pushed back by plasma ( friction ) Walls make thermal plasma motion : Case 2 v w. 1/ p 3 (Deflagration) plasma bulk motion v w true v w false Ryusuke Jinno 05 / 22

12 DYNAMICS AFTER COLLISION Bubbles start to nucleate - Nucleation rate (per unit time & vol) Γ(t) e βt Ryusuke Jinno 06 / 22

13 DYNAMICS AFTER COLLISION Bubbles expand - Bubbles expand, keeping (thickness of bulk motion) (bubble radius) = const. typically ~ Bulk motion carries most of the released energy - Typically collide after nucleation t 1/ Ryusuke Jinno 06 / 22

14 DYNAMICS AFTER COLLISION Bubbles collide - Scalar field damps soon after collision c s v w - Plasma bulk motion continues to propagate sound 2 t c 2 sr 2 u i =0 u i : fluid velocity field Note velocity changes from v w to c s - Thickness of the bulk motion is fixed at the time of collision Ryusuke Jinno 06 / 22

15 DYNAMICS AFTER COLLISION Turbulence develops - Nonlinear effect appears at late times turbulence Ryusuke Jinno 06 / 22

16 THREE SOURCES OF GWS Classification of GW sources GWs h ij T ij [e.g. Caprini et al., JCAP 1604(2016)] 1. Walls (energetically subdominant) collide and damp soon bubble collision 2. Plasma bulk motion continues to propagate sound waves 3. At late times, sound waves develop into nonlinear regime turbulence Ryusuke Jinno 07 / 22

17 THREE SOURCES OF GWS Classification of GW sources GWs hij Tij 1. Walls (energetically subdominant) collide and damp soon bubble collision [Hindmarsh et al. 15] 2. Plasma bulk motion continues to propagate sound waves 3. At late times, sound waves develop into nonlinear regime turbulence Ryusuke Jinno 07 / 22

18 NECESSITY OF ANALYTIC APPROACH What we do when we predict GWs in particle physics models Particle physics model Parameters relevant to phase transition Prediction on GWs e.g. - Transition temperature - Nucleation rate... and so on I want to make our understanding on two-wheel : Numerical understanding + Analytic understanding Why? Imagine any successful field of physics e.g. CMB, lattice QCD,... Ryusuke Jinno 08 / 22

19 TALK PLAN 0. Introduction 1. Bubble dynamics in first-order phase transitions 2. Analytic approach to GW production 3. Future prospects Ryusuke Jinno / 22

20 THE SYSTEM WE WANT TO UNDERSTAND Let us solve the following system Ryusuke Jinno 09 / 22

21 THE SYSTEM WE WANT TO UNDERSTAND Let us solve the following system - Cosmic expansion neglected - Bubbles nucleate with rate Γ (Typically Γ ~ e βt in thermal transitions) - Bubble shells (parametrizing both scalar & plasma bulk motion) are approximated to be thin Ryusuke Jinno 09 / 22

22 THE SYSTEM WE WANT TO UNDERSTAND Let us solve the following system - Shells become more and more energetic T ij (bubble radius) - They lose energy & momentum after first collision T ij 2 (bubble collision) T collision (bubble radius) 2 (arbitrary damping func. D) Ryusuke Jinno 09 / 22

23 THIS SYSTEM IS SOLVABLE We wrote down GW spectrum in this system analytically, essentially from causality : (1 year and half) Full derivation takes too long we illustrate the derivation in a simplified setup : Envelope approximation Ryusuke Jinno 10 / 22

24 n DEFINITION OF GW SPECTRUM Let s focus on transition time, since redshift after production is trivial Transition time Redshift t t = t start t = t end t = t 0 What we want to know : GW (t end,k) = GW energy density per each wavenumber k GW (t end,k) h ij (t end,k)h ij(t end,k) Z tend t start dt x Z tend t start dt y cos(k(t x t y )) F.T. [ht ij (t x, x)t ij (t y, y)i] EM tensor (indices omitted) T (t x,k) T (t y,k) Green(t end,t x ) Green(t end,t y ) h(t end,k) h(t end,k) GW (t end,k) [e.g. Caprini et al., PRD77 (2008)] Ryusuke Jinno 11 / 22

25 DEFINITION OF GW SPECTRUM Let s focus on transition time, since redshift after production is trivial What we want to know : GW (t end,k) EM tensor (indices omitted) Transition time Redshift t = t start t = t end t = t 0 h ij (t end,k)h ij(t end,k) T (t x,k) T (t y,k) Ryusuke Jinno 11 / 22 Message GW spectrum GW (t end,k) is essentially = GW energy density per each wavenumber k two-point Z tend ensemble Z tend average < T T > t start dt x t start dt y cos(k(t x t y )) F.T. [ht ij (t x, x)t ij (t y, y)i] Green(t end,t x ) h(t end,k) h(t end,k) Green(t end,t y ) n t GW (t end,k) [e.g. Caprini et al., PRD77 (2008)]

26 CALCULATION OF htti [Jinno & Takimoto 16 & 17] Calculating means... ht (t x, ~x)t (t y, ~y)i ense - Fix spacetime points x =(t x, ~x) and y =(t y, ~y) - Find bubble configurations s.t. EM tensor T is nonzero at x & y ~x ~y ~x ~y at time t x at time t y nucleation point - Calculate probability value of T (t x, ~x)t (t y, ~y) for such configurations and sum up Ryusuke Jinno 12 / 22

27 CALCULATION OF htti [Jinno & Takimoto 16 & 17] Only two types of configurations exist : - Single-bubble ~x ~y at time t x at time t y nucleation point - Double-bubble ~x ~y Ryusuke Jinno 13 / 22

28 FINAL RESULT FOR ENVELOPE CASE The spectrum becomes sum of two contributions GW (t end,k) / (s) + (d) - Single-bubble spectrum - Double-bubble spectrum Ryusuke Jinno 14 / 22

29 BEYOND THE ENVELOPE Interception (= collision) complicates the calculation once we consider beyond the envelope intercepted walls unintercepted walls Ryusuke Jinno 15 / 22

30 BEYOND THE ENVELOPE: FINAL EXPRESSIONS Full expression reduces to only ~10-dim. integration [Jinno & Takimoto 17] 1. single-bubble + 2. double-bubble Ryusuke Jinno 16 / 22

31 BEYOND THE ENVELOPE: FINAL EXPRESSIONS Full expression reduces to only ~10-dim. integration [Jinno & Takimoto 17] 1. single-bubble General nucleation rate & wall velocity General damping function after collision T ij / (bubble radius) Ryusuke Jinno 16 / 22-2 D

32 BEYOND THE ENVELOPE: FINAL EXPRESSIONS Full expression reduces to only ~10-dim. integration [Jinno & Takimoto 17] 1. single-bubble + 2. double-bubble Ryusuke Jinno 16 / 22

33 NUMERICAL RESULT Single-bubble (Damping function, : interception time) D = e (t t i)/ t i Long duration Envelope coincide with [Huber&Konstandin 08] within factor 2 Ryusuke Jinno 17 / 22

34 NUMERICAL RESULT Single-bubble Sourcing saturates for fixed k / k 1 Sourcing moves to low k at late times typical bubble size -1at collisions Ryusuke Jinno 17 / 22

35 NUMERICAL RESULT Double-bubble Ryusuke Jinno 17 / 22

36 PHYSICAL INTERPRETATION Wavenumber k sourced when the typical bubble size grows to ~ 1/k GWs with wavenumber k ~ 1/k Ryusuke Jinno 18 / 22

37 THIN-WALL NUMERICAL SIMULATION Recently cross-checked by thin-wall numerical simulation by Prof. Konstandin / k 1 / k 3 [Konstandin 17] Ryusuke Jinno 19 / 22

38 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM What are the implications of our result to the REAL system? GW amplitude typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

39 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM What are the implications of our result to the REAL system? GW amplitude Low frequency regime High frequency regime (Our results) typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

40 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM GW spectrum discussed in the literature GW amplitude (according to LISA working group) f 3 f 4 H enhancement sound shell grows until Hubble time typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

41 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM GW spectrum discussed in the literature GW amplitude Nonlinear dynamics starts at late times (turbulence) typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

42 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM GW spectrum discussed in the literature GW amplitude Nonlinear dynamics starts at late times (turbulence) typical bubble size typical sound shell size [Caprini et al. 16] GW frequency Ryusuke Jinno 20 / 22

43 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM GW spectrum may be more rich & structureful than previously thought GW amplitude Structure growing to lower frequency f 3 f 4 f 1 f 3 typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

44 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM All these structures tell us about GW spectrum may be more rich & structureful than previously thought the physics which drives the transition GW amplitude f 3 f 4 f 1 f 3 typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

45 IMPLICATIONS: RICH & STRUCTUREFUL SPECTRUM Sound shell model for GW enhancement (for experts) [Hindmarsh 16] GW amplitude Still growing structue to lower frequency f 1 f 3 f 1 typical bubble size typical sound shell size GW frequency Ryusuke Jinno 20 / 22

46 TALK PLAN 0. Introduction 1. Bubble dynamics in first-order phase transitions 2. Analytic approach to GW production 3. Future prospects Ryusuke Jinno / 22

47 FUTURE PROSPECTS Can we make GWs CMB? Many things to do: c s v w - Make more realistic prediction by accommodating propagation velocity change - Cross-check with thin-wall numerical simulations establish low-freq. regime - Subtracting above from full numerical simulation will tell us really β/h enhancing part of sound waves - Other questions e.g. how long sound waves last? We can divide problems into smaller pieces... [Hindmarsh et al. 17] Ryusuke Jinno 21 / 22

48 CONCLUSION We developed an analytic approach to GW production in phase transitions, which will describe the low-frequency regime of GW spectrum Will help to interpret numerical simulation results and to gain insight on the physics encoded in the spectrum Still many things to do: Let s prepare for LISA Ryusuke Jinno 22 / 22

49 Backup

50 SOURCES FOR COSMOLOGICAL GWS Inflationary quantum fluctuations ( primordial GWs ) Preheating (particle production just after inflation) Cosmic strings, Domain walls First-order phase transition can occur in many physics models - Electroweak sym. breaking - PQ sym. breaking (w/ extension) - Breaking of GUT group - B-L breaking - Strong dynamics... and so on Ryusuke Jinno / 22

51 BEHAVIOR OF BUBBLES Two main players : scalar field & plasma [e.g. Espinosa et al., JCAP06(2010)028] pressure scalar+plasma dynamics true friction false wall - Walls (where the scalar field value changes) want to expand ( pressure ) - Walls are pushed back by plasma ( friction ) Pressure & friction are determined by Pressure released ~ ~ / rad rad Friction ~ (coupling btw. scalar field & plasma) v w (wall velocity) Ryusuke Jinno / 22

52 BEHAVIOR OF BUBBLES Pressure vs. friction gives terminal velocity of walls Pressure ~ Walls drag fluid as they propagate increasing in Friction ~ v w v w decreasing in p Large v w ( & 1/ 3 ) : Detonation v w v w true false plasma bulk motion Ryusuke Jinno / 22

53 BEHAVIOR OF BUBBLES Pressure vs. friction gives terminal velocity of walls Pressure ~ Walls drag fluid as they propagate increasing in Friction ~ v w v w decreasing in v w Small (. 1/ p 3 ) : Deflagration v w v w true false plasma bulk motion Ryusuke Jinno / 22

54 BEHAVIOR OF BUBBLES Understanding until ~ 2016 [e.g. Bodeker & Moore, JCAP 0905 (2009) 009 Espinosa et al., JCAP 1006 (2010) 028] & O(0.1) : Large 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 Ryusuke Jinno / 22

55 BEHAVIOR OF BUBBLES Understanding from 2017 ~ [Bodeker & Moore 17] & O(0.1) plasma bulk motion pressure pressure : Large energy release cs wall. O(0.1) plasma bulk motion cs wall friction / w transition splitting : Small energy release friction Runaway High-terminal velocity - Plasma friction does 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 Ryusuke Jinno / 22

56 GRAVITATIONAL WAVES? Transverse-traceless part (tensor part) of the metric (2dof) ds 2 = dt 2 + a 2 (t)( ij +2h ij )dx i dx j h ii i h ij =0 Action is similar to massless scalar Z S grav = d 4 x p gm 2 P apple 1 2ḣ2 ij 1 2a 2 (rh ij) 2 M P h ij : canonical Coupled to the energy-momentum tensor of the system h ij =8 GK ij,kl T kl projection to transverse-traceless modes energy-momentum tensor (coming from bubbles) Ryusuke Jinno / 22

57 FRICTION ON THE WALL 1 1 process wall rest frame symmetric higgs mass m a,s mass m a,h momentum T momentum T - number density γ-enhanced - contribution from each particle γ-suppressed E 2 = m 2 a,s + p 2 z,in E 2 = m 2 a,h + p 2 z,out T 3 1/ T Ryusuke Jinno / 22

58 FRICTION ON THE WALL 1 2 process wall rest frame transition rad. ~ T - number density γ-enhanced - contribution from each particle almost constant in γ mass m a,s mass m a,h momentum T momentum T E 2 = m 2 a,s + p 2 z,in E 2 = m 2 a,h + p 2 z,out Ryusuke Jinno / 22

59 n DEFINITION OF GW SPECTRUM Let s focus on transition time, since redshift after production is trivial Transition time Redshift t t = t start t = t end t = t 0 What we want to know : GW (t end,k) = GW energy density per each wavenumber k GW (t end,k) h ij (t end,k)h ij(t end,k) Z tend t start dt x Z tend t start dt y cos(k(t x t y )) F.T. [ht ij (t x, x)t ij (t y, y)i] EM tensor (indices omitted) T (t x,k) T (t y,k) Green(t end,t x ) Green(t end,t y ) h(t end,k) h(t end,k) GW (t end,k) [e.g. Caprini et al., PRD77 (2008)] Ryusuke Jinno / 22

60 CALCULATION OF htti [Jinno & Takimoto 16 & 17] Calculating means... ht (t x, ~x)t (t y, ~y)i ense - Fix spacetime points x =(t x, ~x) and y =(t y, ~y) - Find bubble configurations s.t. EM tensor T is nonzero at x & y, ~x ~y i.e. bubble shells are on x & y ~x ~y at time t x at time t y nucleation point - Calculate probability for such a configuration to occur value of T (t x, ~x)t (t y, ~y) for such a configuration and sum up Ryusuke Jinno / 22

61 CALCULATION OF htti [Jinno & Takimoto 16 & 17] Only two types of configurations exist : - Single-bubble ~x ~y at time t x at time t y nucleation point - Double-bubble ~x ~y Ryusuke Jinno / 22

62 ILLUSTRATION: SINGLE-BUBBLE SPECTRUM Necessary and sufficient conditions - No bubbles nucleate inside past cones (probability denoted by P (x, y) ) - One bubble nucleates inside the red diamond t = t n slice within infinitesimal time interval t n t n + dt n Resulting expression ht (x)t (y)i (s) ense Z = P (x, y) dt n prob. for one bubble to nucleate in the red diamond value of T (x)t (y) realized in each case Ryusuke Jinno / 22

63 NUMERICAL RESULT FOR ENVELOPE CASE Consistent with numerical simulation within factor ~2 v = 1 v = 0.1 v = 0.01 [Jinno & Takimoto 16] Ryusuke Jinno / 22

64 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 [Jinno & Takimoto, PRD95 (2017)] - In this sense, breaking of spherical sym. is automatically taken into account Ryusuke Jinno / 22

65 SELF INTRODUCTION Name : Ryusuke Jinno / / Career : 2016/3 : Univ. of Tokyo (supervised by Takeo Moroi) 2016/4-8 : JSPS KEK, Tsukuba, Japan 2016/9- : Research IBS-CTPU, Korea Research interest & recent works (~ 1 year) - Inflation : Hillclimbing inflation (unexplored branch of inflatoinary attractor) Hillclimbing Higgs inflation (new realization of Higgs inflation) - (P)reheating : Preheating in Higgs inflation (discovery of main preheating channel) - Gravitational waves : Analytic approach to GW poduction Ryusuke Jinno / 22