Gravitational waves from first-order phase transitions: some developments in ultra-supercooled transitions Ryusuke Jinno (DESY) Based on 1707.03111 with Masahiro Takimoto (Weizmann) 1905.00899 with Hyeonseok Seong (IBS & KAIST), Masahiro Takimoto (Weizmann), Choong Min Um (KAIST) 23.6.2020 @ Heidelberg Univ.
Introduction
GRAVITATIONAL WAVES: PROBE TO THE EARLY UNIVERSE Gravitational waves Transverse-traceless part of the metric ds 2 = − dt 2 + a 2 ( δ ij + h ij ) dx i dx j sourced by the energy-momsntum tensor □ h ij ∼ GT ij GW detections by LIGO & Virgo have been exciting us [Wikipedia "List of gravitational wave observations"] [see also https://gracedb.ligo.org/superevents/public/O3/] Ryusuke Jinno / 1707.03111, 1905.00899 Ryusuke Jinno / 1707.03111, 1905.00899 01 / 29 / 29
FROM ASTROPHYSICAL TO COSMOLOGICAL GWS Space GW antenna [ Slide by Masaki Ando ] B-DECIGO LISA (Deci-hertz Interferometer (Laser Interferometer Gravitational Wave Observatory) Space Antenna) - Target: IMBH, BBH, BNS. - Target: SMBH, Binaries. GWs around 0.1Hz. GWs around 1mHz. - Baseline : 100 km. - Baseline : 2.5M km. Formation flight by 3 S/C. Constellation flight by 3 S/C - Fabry-Perot interferometer. - Optical transponder. Arm cavity Lase Mirror r Photo- detecto Drag-free S/C r YKIS2018a Symposium (Feb. 19th, 2018, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto) Ryusuke Jinno / 1707.03111, 1905.00899 02 / 29
FIRST-ORDER PHASE TRANSITION & GWS Rough sketch of 1st-order phase transition & GW production Bubbles nucleate, expand, collide and disappear, accompanying fluid dynamics Field space Position space false vacuum true vacuum true (“nucleation”) false true released energy V true x 3 Φ Quantum tunneling Bubble formation & GW production Ryusuke Jinno / 1707.03111, 1905.00899 03 / 29
FIRST-ORDER PHASE TRANSITION & GWS Rough sketch of 1st-order phase transition & GW production Bubbles nucleate, expand, collide and disappear, accompanying fluid dynamics Field space Position space GWs ⇤ h ij ∼ T ij false vacuum true vacuum true Bubbles & fluid released true source GWs energy V true x 3 Φ Quantum tunneling Bubble formation & GW production Ryusuke Jinno / 1707.03111, 1905.00899 03 / 29
FIRST-ORDER PHASE TRANSITION & GWS -3 10 ~ 1Hz GWs correpond to electroweak physics and beyond Space Pulsar timing arrays Ground Energy fraction of GWs -8 2 10 Hz 0.001-1Hz 10 Hz GW frequency [Hz] [http://rhcole.com/apps/GWplotter/] Note : Temperature of the Universe β / H * ∼ 10 3 MeV GeV TeV PeV @ transition time Ryusuke Jinno / 1707.03111, 1905.00899 04 / 29
TALK PLAN ✔ 1. Introduction 2. Brief review of bubble dynamics and GW production 3. GW production in ultra-supercooled transitions: Effective description of fluid propagation & Implications to GW production 4. Summary Ryusuke Jinno / 1707.03111, 1905.00899 / 29
BUBBLE DYNAMICS BEFORE COLLISION "Pressure vs. friction" determines behavior of bubbles - Two main players : scalar field and plasma cosmological scale - Walls want to expand (“pressure”) false ρ vac pressure Parametrized by α ≡ [ Several definitions exist... see e.g. wall ρ plasma Giese, Konstandin, van de Vis '20] scalar+plasma - Walls are pushed back by plasma (“friction”) dynamics Parametrized by coupling btwn. scalar and plasma η friction true - Let's see how bubbles behave for different α (with fixed coupling ) η Ryusuke Jinno / 1707.03111, 1905.00899 Ryusuke Jinno / 1707.03111, 1905.00899 04 / 29
BUBBLE DYNAMICS ρ vac α ≡ ρ plasma BEFORE COLLISION [ Espinosa, Konstandin, No, Servant ’10 ] Small (say, ) T / T � Temperature α α ≲ 𝒫 (0.1) “deflagration” 1.2 1.0 0.8 0.6 wall position 1.0 r / t 0.0 0.2 0.4 0.6 0.8 Fluid outward velocity v fluid 0.5 0.4 0.3 0.2 0.1 wall position 1.0 r / t 0.0 0.2 0.4 0.6 0.8 Ryusuke Jinno / 1707.03111, 1905.00899 05 / 29
BUBBLE DYNAMICS ρ vac α ≡ ρ plasma BEFORE COLLISION [ Espinosa, Konstandin, No, Servant ’10 ] Small but slightly increased α Temperature T / T � 1.3 “detonation” 1.2 1.1 1.0 0.9 wall position 1.0 r / t 0.0 0.2 0.4 0.6 0.8 Fluid outward velocity v fluid 0.4 0.3 0.2 0.1 wall position 1.0 r / t 0.0 0.2 0.4 0.6 0.8 Ryusuke Jinno / 1707.03111, 1905.00899 05 / 29
PARAMETERS CHARACTERIZING THE TRANSITION Definition Properties Strength of the transition α ρ vac / ρ plasma Bubble nucleation rate Bubbles collide after nucleation Δ t ∼ 1/ β Taylor-expanded around Δ t β the transition time t * Γ ( t ) ∝ e β ( t − t * ) Typical bubble size ∼ v w Δ t ∼ v w / β Determined by the balance Wall velocity v w btwn. pressure & friction Transition temperature T * Ryusuke Jinno / 1707.03111, 1905.00899 06 / 29
DYNAMICS AFTER COLLISION Bubbles nucleate & expand - Nucleation rate (per unit time & vol) Γ ( t ) ∝ e β ( t − t * ) - Typically the released energy is carried by fluid motion [ Bodeker & Moore ’17 ] - Collide after nucleation Δ t ∼ 1/ β Ryusuke Jinno / 1707.03111, 1905.00899 07 / 29
DYNAMICS AFTER COLLISION Bubbles nucleate & expand - Nucleation rate (per unit time & vol) Γ ( t ) ∝ e β ( t − t * ) - Typically the released energy is carried by fluid motion [ Bodeker & Moore ’17 ] - Collide after nucleation Δ t ∼ 1/ β Ryusuke Jinno / 1707.03111, 1905.00899 07 / 29
⃗ DYNAMICS AFTER COLLISION GWs ⇤ h ij ∼ T ij Bubbles collide - Scalar field damps soon after collision - For small ( ), plasma motion is α ≲ 𝒫 (0.1) well described by linear approximation: “sound waves” ( ∂ 2 t − c 2 s ∇ 2 ) v fluid ≃ 0 - In this case, fluid shell thickness is fixed at the time of collision Ryusuke Jinno / 1707.03111, 1905.00899 Ryusuke Jinno / 1707.03111, 1905.00899 07 / 29
DYNAMICS AFTER COLLISION GWs ⇤ h ij ∼ T ij Turbulence develops - Nonlinear effects becomes important at late times “turbulence” Ryusuke Jinno / 1707.03111, 1905.00899 07 / 29
SOURCES OF GWS IN FIRST-ORDER PHASE TRANSITION Time evolution of the system Bubble nucleation & expansion → Collision → Sound waves → Turbulence Resulting GW spectrum is classified accordingly: [ Caprini et al. 1512.06239 ] Ω GW = Ω (coll) GW + Ω (sw) GW + Ω (turb) GW Typically is the largest, partly because of different parameter dependence: Ω (sw) GW [ Hindmarsh, Huber, Rummukainen, Weir '13, '15, '17 ] ∝ ( 2 − 2 1 + α ) ( H * ) α β Ω (coll) (from scalar walls) GW β Note : ∼ 10 1 − 5 ≫ 1 ∝ ( H * 2 − 1 1 + α ) ( H * ) α β Ω (sw) (from fluid shells) GW Ryusuke Jinno / 1707.03111, 1905.00899 08 / 29
⃗ ⃗ ⃗ ⃗ ⃗ GW ENHANCEMENT BY SOUND WAVES Bubble collision Sound waves v (1) v (2) v (2) v fluid = fluid + fluid fluid v (1) fluid Thick source: sound shells continue to overlap Thin source [ e.g. Huber & Konstandin '08 everywhere during the whole Hubble time Jinno & Takimoto '16 ] [ Hindmarsh '18 ] Difference is huge: [ Hindmarsh and Hijazi '19 ] GW spectrum GW spectrum β / H * ∼ 10 1 − 5 frequency frequency shell shell bubble − 1 bubble − 1 − 1 − 1 ( ( ) ) ( ) ( ) size thickness size thickness Ryusuke Jinno / 1707.03111, 1905.00899 09 / 29
GWS FROM THIN SOUCE (A BIT OF ADVERTISEMENT) GW production from thin source is strictly calculable [ RJ & Takimoto 1707.03111 ] - Cosmic expansion neglected - Bubbles nucleate with rate Γ ( Γ ∝ e β t (Typically in thermal transitions) - Bubbles are approximated to be thin Ryusuke Jinno / 1707.03111, 1905.00899 10 / 29
GWS FROM THIN SOUCE (A BIT OF ADVERTISEMENT) GW production from thin source is strictly calculable [ RJ & Takimoto 1707.03111 ] - Shells become more and more energetic ∝ (bubble radius) T ij - They lose energy & momentum after first collision 2 (bubble radius @ collision) @ collision × T ij T ij = (bubble radius) 2 × (arbitrary damping func. D) Ryusuke Jinno / 1707.03111, 1905.00899 10 / 29
GWS FROM THIN SOUCE (A BIT OF ADVERTISEMENT) GW production from thin source is strictly calculable [ RJ & Takimoto 1707.03111 ] = ∆ ( s ) + ∆ ( d ) ρ GW ( k ) ∝ Ryusuke Jinno / 1707.03111, 1905.00899 11 / 29
GWS FROM THIN SOUCE (A BIT OF ADVERTISEMENT) GW production from thin source is strictly calculable [ RJ & Takimoto 1707.03111 ] = ∆ ( s ) + ∆ ( d ) ρ GW ( k ) ∝ Ryusuke Jinno / 1707.03111, 1905.00899 11 / 29
TALK PLAN ✔ 1. Introduction ✔ 2. Brief review of bubble dynamics and GW production 3. GW production in ultra-supercooled transitions: Effective description of fluid propagation & Implications to GW production 4. Summary Ryusuke Jinno / 1707.03111, 1905.00899 / 29
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