Gravitational waves from early universe phase transitions


David J. Weir - University of Helsinki - davidjamesweir

PRACEdays18, 29 May 2018

What happened when the universe was optically opaque?

Original source: arXiv:1205.2451


  • What are the observable gravitational wave signatures of cosmological processes?
  • What can we say about physics beyond the Standard Model with gravitational waves?


Simulation pipeline from particle theory to GW observation

What's next: LISA

  • Three laser arms, 2.5 M km separation
  • ESA’s L3 mission, launch by 2034
  • Proposal submitted last year 1702.00786
  • Officially adopted on 20.6.2017

First order thermal phase transitions

  1. Higgs 'turns on': bubbles nucleate and grow
  2. Bubbles expand in plasma - reaction fronts form
  3. Bubbles + fronts collide
  4. Sound waves in plasma ➝ GWs
  5. Endgame: turbulence?

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 ...

Coupled field and fluid system

Ignatius, Kajantie, Kurki-Suonio and Laine
  • Scalar $\phi$ (the Higgs) and ideal fluid $u^\mu$ (plasma):
    • Split stress-energy tensor $T^{\mu\nu}$ into field and fluid bits $$\partial_\mu T^{\mu\nu} = \partial_\mu (T^{\mu\nu}_\phi + T^{\mu\nu}_\text{fluid}) = 0$$
    • Parameter $\eta$ sets the scale of friction due to plasma $$\partial_\mu T^{\mu\nu}_\phi = \tilde \eta \frac{\phi^2}{T} u^\mu \partial_\mu \phi \partial^\nu \phi $$
    • Create reaction front in the plasma that propagates outward with the bubble

Velocity profile development: detonation vs deflagration

Dynamic range issues

  • Early universe simulations usually handle one length scale
  • Here, many length scales important

Tier-0 project: Hazel Hen at HLRS

Recent runs: $4200^3$ lattices, 1M CPUh each (17.6M total)

Simulation slice example

Results: GW power spectra, power laws

Fast deflagration



  • LISA will hunt the cosmic gravitational wave background
  • We don't know how the Higgs "turned on" - LISA can help
  • Requires very large, multi-scale simulations
  • PRACE resources ➝ simulations ➝ predictions for LISA
  • Turbulence and much more still to do

Read more: arXiv:1704.05871, arXiv:1705.01783, arXiv:1512.06239.