What are the observable gravitational wave signatures of
cosmological processes?

What can we say about physics beyond the Standard
Model with gravitational waves?

Goal:

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

Higgs 'turns on': bubbles nucleate and grow

Bubbles expand in plasma - reaction fronts form

Bubbles + fronts collide

Sound waves in plasma ➝ GWs

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