Higgsless simulations of cosmological phase transitions and gravitational waves

Abstract: First-order cosmological phase transitions in the early Universe source sound waves and, subsequently, a background of stochastic gravitational waves. Currently, predictions of these gravitational waves rely heavily on simulations of a Higgs field coupled to the plasma of the early Universe, the former providing the latent heat of the phase transition. Numerically, this is a rather demanding task since several length scales enter the dynamics. From smallest to largest, these are the thickness of the Higgs interface separating the different phases, the shell thickness of the sound waves, and the average bubble size. In this work, we present an approach to perform Higgsless simulations in three dimensions, producing fully nonlinear results, while at the same time removing the hierarchically smallest scale from the lattice. This significantly reduces the complexity of the problem and contributes to making our approach highly efficient. We provide spectra for the produced gravitational waves for various choices of wall velocity and strength of the phase transition, as well as introduce a fitting function for the spectral shape.