  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.
