First-order phase transitions

David J. Weir - University of Helsinki - davidjamesweir
On behalf of the LISA Cosmology Working Group

LISA Symposium, 12 July 2018

Electroweak phase transition

  • Process by which the Higgs 'switched on'
  • In the Standard Model it is gentle (crossover)
  • Possible (and theoretically attractive) in extensions that it would experience a first order phase transition

Source: Morrissey and Ramsey-Musolf


Why study first-order [electroweak] phase transitions?

  • Connects the biggest mysteries in modern physics:
    • Baryogenesis and baryon asymmetry
    • Origin of mass - Higgs mechanism
    • Dark matter? Inflation? Neutrino masses?
  • Difficult to probe the conditions of the EWPT at colliders
  • Use gravitational waves to see what happened:
    • Then: bubble radius (length scale) close to $1/H_*$
      Now: characteristic frequency mHz

First order thermal phase transitions

  1. Bubbles nucleate and grow
  2. Expand in a plasma - reaction fronts form
  3. Bubbles + fronts collide - violent process
  4. Sound waves left behind in plasma
  5. Endgame: shocks; turbulence? [Next talk]

What [still] has a first-order PT?

  • Higgs singlet model - add extra real singlet field $\sigma$:
    difficult to rule out with colliders [arXiv:1704.05844]
  • Two Higgs doublet model - add second complex doublet:
    many parameters, quite constrained [arXiv:1405.5537]
  • Triplet models - add adjoint scalar field (triplet):
    few parameters, not widely studied [arXiv:1802.10500]
  • And many, many more...

All have unexcluded regions of parameter space for which the phase transition is first order.

CosWG report [arXiv:1512.06239]

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

Current PT work in LISA CosWG

  • In preparation: update to first report on PTs
    • Updated 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: early autumn 😅

New "PTPlot" tool

Complementarity and multiband

  • Breakthrough possibility:
    See new physics first, if no deviations seen at LHC
    • The three cases (singlet, doublet, triplet) from earlier all have regions that produce first-order phase transitions, that will not be ruled out by HL-LHC.
    • Phase transitions produce substantial backgrounds across wide range of frequencies
    • Use full network of SKA, LISA, ET and aLIGO-aVIRGO-KAGRA to constrain parameter space
    • Reconstruct parameters: guide collider experiments

[see Germano Nardini's poster] + arXiv:1806.06463

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

[Late-time behaviour? See next talk]


  • The electroweak phase transition is 'wide open':
    • Colliders cannot (currently) rule out some scenarios
    • Baryogenesis, dark matter, ...
  • LISA will be able to detect (or rule out) various scenarios!
  • Understanding of first-order phase transitions improving
    • Models and parameter spaces
    • Microscopic dynamics of the transition
    • Gravitational wave power spectrum

You may view this talk later at:

More info: arXiv:1705.01783