First order phase transitions beyond the Standard Model

The direct detection of gravitational waves by the LIGO/Virgo collaboration shows that a new window on the
Universe is now open, with the potential to revolutionise our knowledge of its history. Equally, the discovery
of the Higgs particle at the Large Hadron Collider (LHC) has triggered a hunt for a complete understanding of
the origin of elementary particle masses. These most fundamental strands of physics are linked in the early
Universe at around 10 picoseconds, when the electroweak phase transition took place, and the Higgs field
"turned on". This process could have been a violent one, generating gravitational waves detectable by spacebased
gravitational wave detectors with sensitivity in the millihertz band. The European Space Agency has
recently approved just such a mission, Laser Interferometer Space Antenna (LISA), which will launch by
2034. LISA has the potential to directly probe of the conditions of the Universe at an age of about 10
picoseconds, and at the same time the physics of mass generation. .
An early Universe first-order phase transition is characterised as follows. The energy scale is set by the
critical temperature Tc, below which bubbles of the Higgs phase can spontaneously nucleate and grow. The
bubble nucleation rate per unit volume is calculable in terms of the transition rate parameter b, the rate of the
change of the activation barrier. The third parameter a is roughly the potential energy in the Higgs field
relative to the thermal energy, which controls the fluid shear stresses, the source for the gravitational waves.
The efficiency depends on the final parameter, the speed with which the phase boundary expands vw.
There is a strong drive towards the determination of the gravitational wave power spectrum as a function of
the parameters (Hn,a,b,vw), This project aims to link this programme back to fundamental physics by
improving the computation of the parameters (Hn,a,b,vw) from the masses and coupling constants of
underlying particle physics models, so that the power spectrum can be computed with 20% accuracy.
The wall speed vw is the parameter with the most uncertainty, up to a factor two for low values. This project
will develop and apply new methods to improve the accuracy of the vw calculation to the required 5% level.
Lattice Monte Carlo techniques have good potential, as they treat properly the IR modes of the W and Z
fields which are the source of significant uncertainty. The project will explore the use the holographic
approach to strongly-interacting field theories to compute the thermal activation rate from a solution to the
dual 5-dimensional gravitational theory.