We study the energy budget of a first-order cosmological phase transition, which is an important factor in the prediction of the resulting gravitational wave spectrum. Formerly, this analysis was based mostly on simplified models as for example the bag equation of state. Here, we present a model-independent approach that is exact up to the temperature dependence of the speed of sound in the broken phase. We find that the only relevant quantities that enter in the hydrodynamic analysis are the speed of sound in the broken phase and a linear combination of the energy and pressure differences between the two phases which we call pseudotrace (normalized to the enthalpy in the broken phase). The pseudotrace quantifies the strength of the phase transition and yields the conventional trace of the energy-momentum tensor for a relativistic plasma (with speed of sound squared of one third).We study this approach in several realistic models of the phase transition and also provide a code snippet that can be used to determine the efficiency coefficient for a given phase transition strength and speed of sound. It turns out that our approach is accurate to the percent level for moderately strong phase transitions, while former approaches give at best the right order of magnitude.

We provide an easy method to obtain the kinetic energy fraction in gravitational waves, generated during a cosmological first-order phase transition, as a function of only the wall velocity and quantities that can be determined from the particle physics model at the nucleation temperature. This generalizes recent work that achieved this goal for detonations. Here we present the corresponding results for deflagrations and hybrids. Unlike for detonations, the sound speed in the symmetric phase also enters the analysis. We perform a detailed comparison between our model-independent approach and other approaches in the literature. We provide a Python code snippet to determine the kinetic energy fraction K as a function of the wall velocity, the two speeds of sound and the strength parameter of the phase transition. We also assess how realistic sizable deviations in speed of sound are close to the phase transition temperature in a specific model.

We study to what extent LISA can observe features of gravitational wave spectra originating from cosmological first-order phase transitions. We focus on spectra which are of the form of double-broken power laws. These spectra are predicted by hydrodynamic simulations and also analytical models such as the sound shell model. We argue that the ratio of the two break frequencies is an interesting observable since it can be related to the wall velocity while overall amplitude and frequency range are often degenerate for the numerous characteristics of the phase transition. Our analysis uses mock data obtained from the power spectra predicted by the simplified simulations and the sound shell model and analyzes the detection prospects using χ 2 -minimization and likelihood sampling. We point out that the prospects of observing two break frequencies from the electroweak phase transition is hindered by a shift of the spectrum to smaller frequencies for strong phase transitions. Finally, we also highlight some differences between signals from the sound shell model compared to simulations.

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