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

1/21

Lots of potential sources. . . . . . lots of potential detectors . . .

LISA Pathfinder exceeds expectations

2/21

Exceeded design expectations by a factor of five! Close to requirements for LISA.

What’s next: LISA

3/21

• 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

From the proposal

4/21

While they build the machine, we need to build the models and theories. . .

Thermal phase transitions 1

5/21

• 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

• Standard Model is a crossover

Kajantie et al.; Csikor et al.; . . .

• First order still possible in extensions

(singlet, 2HDM, . . . )

Andersen et al., Kozaczuk et al., Carena et al., B¨

• deker et al., Damgaard et al., Ramsey-Musolf et al.,

Cline and Kainulainen. . .

• Baryogenesis?
• GW power spectrum ⇔ model information?

T mH

Symmetric phase Higgs phase supercritical condensation 75 GeV 125 GeV

Thermal phase transitions 2

6/21

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 αT∗

• Friction from plasma acts on bubble walls

– walls move with velocity vwall

• Bubbles interact with plasma

– deposit KE with efficiency κf(αT∗, vwall)

• Bubbles collide

– producing gravitational waves

β, αT∗, vwall (and T∗):

3 (+1) parameters are all you need

Espinosa, Konstandin, No, Servant; Kamionkowski, Kosowsky, Turner

What the metric sees at a thermal phase transition

7/21

• Bubbles nucleate, most energy goes into plasma, then:

1.

h2Ωφ: Bubble walls and shocks collide

– ‘envelope phase’ 2.

h2Ωsw: Sound waves set up after bubbles have collided

– ‘acoustic phase’ 3.

h2Ωturb: [MHD] turbulence

– ‘turbulent phase’

• These sources then add together to give the observed GW power:

h2ΩGW ≈ h2Ωφ + h2Ωsw + h2Ωturb

1: Envelope approximation

Kosowsky, Turner and Watkins; Kamionkowski, Kosowsky and Turner 8/21

• Thin, hollow bubbles, no fluid
• Stress-energy tensor ∝ R3 on wall
• Keep track of solid angle;
• verlapping bubbles → GWs
• Simple power spectrum:
• One length scale

(average bubble radius R∗)

• Two power laws (ω3, ∼ 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)

1: Envelope approximation

Huber and Konstandin 9/21

4-5 numbers parametrise the transition:

• αT∗, vacuum energy fraction
• vw, bubble wall speed
• κφ, conversion ‘efficiency’ into

gradient energy (∇φ)2

• Transition rate:
• H∗, Hubble rate at transition
• β, bubble nucleation rate

→ ansatz for h2Ωφ

0.001 0.01 0.1

k (Tc)

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1

d ln ρGW/d ln k (G Tc

6)

k~l

• 1

k~L

• 1

[generally subdominant, except for vacuum/runaway transitions]

2: Coupled field and fluid system

10/21

• Scalar φ + ideal fluid uµ
• Split stress-energy tensor T µν into field and fluid bits

Ignatius, Kajantie, Kurki-Suonio and Laine

∂µT µν = ∂µ(T µν

field + T µν fluid) = 0

• Parameter η sets the scale of friction due to plasma

∂µT µν

field = ˜

η φ2

T uµ∂µφ∂νφ

∂µT µν

fluid = −˜

η φ2

T uµ∂µφ∂νφ

• V (φ, T) is a ‘toy potential’ tuned to give latent heat L
• β ↔ number of bubbles, αT∗ ↔ L, vwall ↔ ˜

η

Begin in spherical coordinates: what sort of solutions does this system have?

2: Velocity profile development - detonation

11/21

Small ˜

η ⇒ detonation (supersonic wall)

0.5 0.6 0.7 cs

ξ=r/t

0.01 0.02 0.03

v η=0.1 t=500/Tc t=1000/Tc Late times

2: Velocity profile development - deflagration

12/21

Large ˜

η ⇒ deflagration (subsonic wall)

0.3 0.4 0.5 0.6 cs

ξ=r/t

0.01 0.02 0.03

v η=0.2 t=500/Tc t=1000/Tc Late times

2: Simulation slice example]

13/21

2: Velocity power spectra and power laws

14/21

Fast deflagration Detonation

• Weak transition: αTN = 0.01
• Power law behaviour above peak is between k−2 and k−1
• “Ringing” due to simultaneous bubble nucleation, not physically important

2: GW power spectra and power laws

15/21

Fast deflagration Detonation

• Approximate k−3 to k−4 power spectrum at high k
• Expect causal k3 at low k
• Curves scaled by t: source ‘on’ continuously until turbulence/expansion

→ power law ansatz for h2Ωsw

3: Transverse versus longitudinal modes – turbulence?

16/21

100 101 102 kR∗ 10−12 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−4 dV 2/d log k

Nb = 84, 42003, η = 0.19, vw = 0.92, φ2/T parameters, velocity power Longitudinal Transverse

• 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 h2Ωturb

Putting it all together - h2Ωgw 1512.06239

17/21

• Three sources, ≈ h2Ωφ, h2Ωsw, h2Ωturb
• Know their dependence on T∗, αT , vw, β
• Know these for any given model, predict the signal. . .

(example with T∗ = 100GeV, αT∗ = 0.5, vw = 0.95, β/H∗ = 10)

Putting it all together - physical models to GW power spectra

18/21

Map your favourite theory to (T∗, αT∗, vw, β); we can put it on a plot like this . . . and tell you if it is detectable by LISA (see 1512.06239)

Preliminary – detectability from acoustic waves alone

19/21

• In many cases, sound waves dominant
• RMS fluid velocity Uf and bubble radius R∗ most important parameters

(quite easily get these from a given model) Espinosa, Konstandin, No and Servant Sensitivity plot:

−4.0 −3.5 −3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0

log10(HnR∗)

−2.00 −1.75 −1.50 −1.25 −1.00 −0.75 −0.50 −0.25

log10 ¯ Uf

1 5 1 20 50 1 0.01 0.1 1 10

Text

PRELIMINARY

More turbulence

The pipeline

20/21

1. Choose your model (e.g. SM, xSM, 2HDM, . . . ) 2. Dimensionally reduced model

Kajantie et al.

3. Phase diagram, nonperturbatively

Kajantie et al. (get αT∗ and T∗)

4. Nucleation rate, nonperturbatively

Moore and Rummukainen (get β)

5. Wall velocities e.g. from Boltzmann equations

Konstandin et al. (get vwall)

6. Gravitational wave PS 7. [Sphaleron rate, nonperturbatively for extra credit Moore ] Currently very leaky even for SM!

Questions, requests or demands. . .

21/21

• 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?