Gravitational waves from a first order electroweak phase transition - PowerPoint PPT Presentation

Gravitational waves from a first order electroweak phase transition PRL 112, 041301 (2014) [arXiv:1304.2433], PRD 92, 123009 (2015) [arXiv:1504.03291], JCAP 1604 (2016) 001 [arXiv:1512.06239], and PRD 93, 124037 (2016) [arXiv:1604.08429]. David J. Weir University of Helsinki Chicheley Hall, 28 March 2017

Gravitational wave sources Lots of potential sources. . . . . . lots of potential detectors . . . 1/21

LISA Pathfinder exceeds expectations Exceeded design expectations by a factor of five! Close to requirements for LISA. 2/21

What’s next: LISA • LISA: three arms (six laser links), 2.5 M km separation • Launch as ESA’s third large-scale mission (L3) in (or before) 2034 • Proposal officially submitted earlier this year 1702.00786 3/21

From the proposal While they build the machine, we need to build the models and theories. . . 4/21

Thermal phase transitions 1 • First order phase transition: 1. Bubbles nucleate and grow 2. Expand in a plasma - create shock waves 3. Bubbles+shocks collide - violent process 4. Sound waves left behind in plasma 125 GeV supercritical • Standard Model is a crossover 75 GeV Kajantie et al.; Csikor et al.; . . . m H Higgs phase • First order still possible in extensions condensation (singlet, 2HDM, . . . ) Symmetric phase Andersen et al. , Kozaczuk et al. , Carena et al. , T B¨ odeker et al. , Damgaard et al. , Ramsey-Musolf et al. , Cline and Kainulainen. . . • Baryogenesis? • GW power spectrum ⇔ model information? 5/21

Thermal phase transitions 2 Extended Standard Model with first-order PT. Around temperature T ∗ , • Bubbles nucleate in false vacuum – with rate β • Bubbles expand, liberate latent heat – characterised by α T ∗ • Friction from plasma acts on bubble walls – walls move with velocity v wall • Bubbles interact with plasma – deposit KE with efficiency κ f ( α T ∗ , v wall ) • Bubbles collide – producing gravitational waves β , α T ∗ , v wall (and T ∗ ): 3 (+1) parameters are all you need Espinosa, Konstandin, No, Servant; Kamionkowski, Kosowsky, Turner 6/21

What the metric sees at a thermal phase transition • Bubbles nucleate, most energy goes into plasma, then: h 2 Ω φ : Bubble walls and shocks collide 1. – ‘envelope phase’ h 2 Ω sw : Sound waves set up after bubbles have collided 2. – ‘acoustic phase’ h 2 Ω turb : [MHD] turbulence 3. – ‘turbulent phase’ • These sources then add together to give the observed GW power: h 2 Ω GW ≈ h 2 Ω φ + h 2 Ω sw + h 2 Ω turb 7/21

1: Envelope approximation Kosowsky, Turner and Watkins; Kamionkowski, Kosowsky and Turner • Thin, hollow bubbles, no fluid Stress-energy tensor ∝ R 3 on wall • • Keep track of solid angle; overlapping bubbles → GWs • Simple power spectrum: • One length scale (average bubble radius R ∗ ) Two power laws ( ω 3 , ∼ ω − 1 ) • • Amplitude ⇒ 4 numbers define spectral form NB: Used to be applied to shock waves (fluid KE), now only use for bubble wall (field gradient energy) 8/21

1: Envelope approximation Huber and Konstandin 4-5 numbers parametrise the transition: 0.1 α T ∗ , vacuum energy fraction • 0.01 6 ) v w , bubble wall speed • d ln ρ GW /d ln k ( G T c 0.001 κ φ , conversion ‘efficiency’ into • 0.0001 gradient energy ( ∇ φ ) 2 1e-05 • Transition rate: 1e-06 H ∗ , Hubble rate at transition • 1e-07 β , bubble nucleation rate • 0.001 -1 0.01 0.1 -1 k ~ L k ~ l k ( T c ) → ansatz for h 2 Ω φ [generally subdominant, except for vacuum/runaway transitions] 9/21

2: Coupled field and fluid system Scalar φ + ideal fluid u µ • Split stress-energy tensor T µν into field and fluid bits • Ignatius, Kajantie, Kurki-Suonio and Laine ∂ µ T µν = ∂ µ ( T µν field + T µν fluid ) = 0 Parameter η sets the scale of friction due to plasma • η φ 2 η φ 2 ∂ µ T µν ∂ µ T µν T u µ ∂ µ φ∂ ν φ T u µ ∂ µ φ∂ ν φ field = ˜ fluid = − ˜ V ( φ, T ) is a ‘toy potential’ tuned to give latent heat L • β ↔ number of bubbles, α T ∗ ↔ L , v wall ↔ ˜ η • Begin in spherical coordinates: what sort of solutions does this system have? 10/21

2: Velocity profile development - detonation Small ˜ η ⇒ detonation (supersonic wall) η =0.1 0.03 t =500/ T c t =1000/ T c Late times 0.02 v 0.01 0 c s 0.5 0.6 0.7 ξ = r/t 11/21

2: Velocity profile development - deflagration Large ˜ η ⇒ deflagration (subsonic wall) η =0.2 0.03 0.02 Late times v t =1000/ T c 0.01 t =500/ T c 0 c s 0.3 0.4 0.5 0.6 ξ = r/t 12/21

2: Simulation slice example] 13/21

2: Velocity power spectra and power laws Fast deflagration Detonation Weak transition: α T N = 0 . 01 • Power law behaviour above peak is between k − 2 and k − 1 • • “Ringing” due to simultaneous bubble nucleation, not physically important 14/21

2: GW power spectra and power laws Fast deflagration Detonation Approximate k − 3 to k − 4 power spectrum at high k • Expect causal k 3 at low k • Curves scaled by t : source ‘on’ continuously until turbulence/expansion • → power law ansatz for h 2 Ω sw 15/21

3: Transverse versus longitudinal modes – turbulence? N b = 84 , 4200 3 , � η = 0 . 19 , v w = 0 . 92 , φ 2 /T parameters, velocity power 10 − 4 10 − 5 10 − 6 10 − 7 d V 2 / d log k 10 − 8 10 − 9 10 − 10 10 − 11 Longitudinal Transverse 10 − 12 10 0 10 1 10 2 kR ∗ • Short simulation; weak transition (small α ): physics is linear; most power is in the longitudinal modes ⇒ acoustic waves, not turbulence Turbulence requires longer timescales R ∗ /U f • • Plenty of theoretical results, use those instead Kahniashvili et al.; Caprini, Durrer and Servant; Pen and Turok; . . . → power law ansatz for h 2 Ω turb 16/21

Putting it all together - h 2 Ω gw 1512.06239 Three sources, ≈ h 2 Ω φ , h 2 Ω sw , h 2 Ω turb • Know their dependence on T ∗ , α T , v w , β • • Know these for any given model, predict the signal. . . (example with T ∗ = 100GeV , α T ∗ = 0 . 5 , v w = 0 . 95 , β/H ∗ = 10 ) 17/21

Putting it all together - physical models to GW power spectra Map your favourite theory to ( T ∗ , α T ∗ , v w , β ) ; we can put it on a plot like this . . . and tell you if it is detectable by LISA (see 1512.06239 ) 18/21

Preliminary – detectability from acoustic waves alone • In many cases, sound waves dominant RMS fluid velocity U f and bubble radius R ∗ most important parameters • (quite easily get these from a given model) Espinosa, Konstandin, No and Servant Sensitivity plot: PRELIMINARY 5 − 0 . 25 0.1 1 50 0 − 0 . 50 1 1 0 1 0 − 0 . 75 U f log 10 ¯ − 1 . 00 0.01 Text 20 − 1 . 25 10 − 1 . 50 More turbulence − 1 . 75 − 2 . 00 − 4 . 0 − 3 . 5 − 3 . 0 − 2 . 5 − 2 . 0 − 1 . 5 − 1 . 0 − 0 . 5 0 . 0 log 10 ( H n R ∗ ) 19/21

The pipeline 1. Choose your model (e.g. SM, xSM, 2HDM, . . . ) 2. Dimensionally reduced model Kajantie et al. 3. Phase diagram, nonperturbatively Kajantie et al. (get α T ∗ and T ∗ ) 4. Nucleation rate, nonperturbatively Moore and Rummukainen (get β ) 5. Wall velocities e.g. from Boltzmann equations Konstandin et al. (get v wall ) 6. Gravitational wave PS 7. [Sphaleron rate, nonperturbatively for extra credit Moore ] Currently very leaky even for SM! 20/21

Questions, requests or demands. . . • Turbulence • MHD or no MHD? Timescales H ∗ R ∗ /U f ∼ 1 , sound waves and turbulence? • • More simulations needed? • Baryogenesis • Competing wall velocity dependence of BG and GWs? • Sphaleron rates in extended models? • Nonperturbative calculations for xSM, 2HDM, triplet model, . . . • What is the phase diagram? • Nonperturbative nucleation rates? 21/21