Higgs physics and cosmology:
Gravitational waves from the EWPT

saoghal.net/slides/charged2018/

David J. Weir - University of Helsinki - davidjamesweir

cHarged 2018±

What happened when the universe was optically opaque?

Source: arXiv:1205.2451

What's next: LISA mission

  • 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

LISA Pathfinder

Exceeded design expectations by factor of five!

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

Possible signals

Source: arXiv:1702.00786.

Key science for LISA

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 ...

Electroweak phase transition


Source: arXiv:1206.2942

First order thermal phase transition

  1. Bubbles nucleate and grow
  2. Expand in a plasma - create reaction fronts
  3. Bubbles + fronts collide - violent process
  4. Sound waves left behind in plasma
  5. Turbulence; damping

Key parameters for GW production

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

How the bubble wall moves

$$ \overbrace{\partial_\mu T^{\mu\nu}}^\text{Force on $\phi$} - \overbrace{\int \frac{d^3 k}{(2\pi)^3} f(\mathbf{k}) F^\nu }^\text{Force on particles}= 0 $$

Phys. Rev. D 46, 2668

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 $u^\mu$.

Detonations vs deflagrations

  • 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

Velocity profile development: detonation vs deflagration

Simulation slice example

Putting it all together - $h^2 \Omega_\text{gw}$

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

CosWG report arXiv:1512.06239

  • 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

Current EWPT work in LISA CosWG

  • 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 😅

PTPlot.org

Recent results 1: parameter space

  • "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

Recent results 2: spectral shape

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

A pipeline

  1. Choose your model (e.g. SM, xSM, 2HDM, ...)
  2. Dim. red. model
    Kajantie et al.
  3. Phase diagram ($\alpha_{T_*}$, $T_*$);
    lattice: Kajantie et al.
  4. Nucleation rate ($\beta$);
    lattice: Moore and Rummukainen
  5. Wall velocities ($v_\text{wall}$)
    Moore and Prokopec; Kozaczuk
  6. GW power spectrum $\Omega_\mathrm{gw}$
  7. Sphaleron rate

Very leaky, even for SM!

What I am thinking about

  • 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?

Final conclusion

  • 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 $100~\mathrm{GeV}$