Gravitational waves from the EWPT

David J. Weir - University of Helsinki - davidjamesweir

cHarged 2018±

Source: arXiv:1205.2451

- Three laser arms, 2.5 M km separation
- ESA-NASA mission, launch by 2034
- Proposal submitted last year arXiv:1702.00786
- Officially adopted on 20.6.2017

Exceeded design expectations by factor of five!

Source: (CC-BY) Phys. Rev. Lett. 116, 231101

Source: arXiv:1702.00786.

Science Investigation 7.2: Measure, or set upper limits on, the spectral shape of the cosmological stochastic GW background.

Operational Requirement 7.2:Probe a broken power-law stochastic background from the early Universe as predicted, for example, by first order phase transitions ...

Source: arXiv:1206.2942

- Bubbles nucleate and grow
- Expand in a plasma - create reaction fronts
- Bubbles + fronts collide - violent process
**Sound waves**left behind in plasma- Turbulence; damping

4 numbers parametrise the transition:

- $T_*$, temperature ($\approx T_\mathrm{n} \lesssim T_\mathrm{c}$)
- $\alpha_{T_*}$, vacuum energy fraction
- $v_\mathrm{w}$, bubble wall speed
- $\beta/H_*$:
- $\beta$, inverse phase transition duration
- $H_*$, Hubble rate at transition

This equation is the realisation of this idea:

Yet another interpretation:

$$ \overbrace{\partial_\mu T^{\mu\nu}}^\text{Field part} - \overbrace{\int \frac{d^3 k}{(2\pi)^3} f(\mathbf{k}) F^\nu }^\text{Fluid part}= 0 $$i.e.:

$$ \partial_\mu T^{\mu\nu}_\phi + \partial_\mu T^{\mu\nu}_\text{fluid} = 0 $$Can simulate as effective model of field $\phi$ + fluid $u^\mu$.

- If $\phi$ wall moves
*supersonically*and the fluid $u^\mu$ enters the wall at rest, we have a*detonation*

☛ Good for GWs, bad for BG - If $\phi$ wall moves
*subsonically*and the fluid $u^\mu$ enters the wall at its maximum velocity, it's a*deflagration*

☛ Bad for GWs, good for BG

- For any given theory, can get $T_*$, $\alpha_{T_*}$, $\beta/H_*$, $v_\mathrm{w}$ arXiv:1004.4187
- It's then easy to predict the signal...

(example, $T_* = 94.7~\mathrm{GeV}$, $\alpha_{T_*} = 0.066$, $v_\mathrm{w} =0.95$, $\beta/H_* = 105.9$) $\mathrm{SNR} = 95$ ☺️

- Results for a variety of models, at "benchmark points"
- Key result: parametric plots with contours at $\mathrm{SNR}_\text{thr}$

Model ⟶ ($T_*$, $\alpha_{T_*}$, $v_\mathrm{w}$, $\beta$) ⟶ SNR

- In preparation: update to first report on PTs (arXiv:1512.06239)
- "Final" sensitivity curve
- Updated model 'showcase'
- New theoretical work (including no runaways)

- PTPlot web tool for computing SNR
- Modular, containerised
- Code will be open, can be run locally

- Coming soon 😅

- "Non-perturbative" results for triplet model arXiv:1802.10500
- Dimensional reduction, mapping to existing theory
- Light green region - first order phase transition
- Dark green + gray regions - new simulations required

- Each simulation: ~1M CPU hours arXiv:1704.05871
- Validate spectral shape used in WG reports

➡

- Choose your model (e.g. SM, xSM, 2HDM, ...)
- Dim. red. model

Kajantie et al. - Phase diagram ($\alpha_{T_*}$, $T_*$);

lattice: Kajantie et al. - Nucleation rate ($\beta$);

lattice: Moore and Rummukainen - Wall velocities ($v_\text{wall}$)

Moore and Prokopec; Kozaczuk - GW power spectrum $\Omega_\mathrm{gw}$
- Sphaleron rate

Very leaky, even for SM!

- Turbulence
- MHD or no MHD?
- Timescales $H_* R_*/\overline{U}_\mathrm{f} \sim 1$, sound waves and turbulence?
- More simulations needed?

- Complementarity of GW signal and BG
- Competing wall velocity dependence of BG and GWs?
- Sphaleron rates in extended models?

- The best possible determinations for xSM, 2HDM,
$\Sigma$SM, ...
- What is the phase diagram?
- Nonperturbative nucleation rates?

- Now have good understanding of thermal history of first-order electroweak phase transitions
- Can make good estimates of the GW power spectrum
- Turbulence still a challenge
- Recently appreciated contributions, like acoustic waves, enhance the source considerably.
- LISA provides a model-independent probe of first-order phase transitions around $100~\mathrm{GeV}$