The effect of sound speed on the gravitational wave spectrum of first order phase transitions in the early universe

TL;DR

This work tackles how a temperature- and phase-dependent sound speed $c_s(T,φ)$ influences the gravitational wave spectrum from first-order phase transitions in the early universe. It extends the PTtools framework to arbitrary equations of state using the Sound Shell Model, linking fluid-shell dynamics to the GW signal and translating it to today’s observable spectrum relevant for LISA. The study shows that moving beyond the ultrarelativistic bag-model assumption significantly reshapes the GW spectrum and its detectability, while preserving a computationally efficient pipeline. By providing an open-source, adaptable toolchain, the work enables robust exploration of phase-transition signals across a broad class of beyond-Standard-Model scenarios.

Abstract

Gravitational waves from first-order phase transitions are a promising probe of physics beyond the Standard Model, as many extensions of the standard model result in first-order phase transitions in the early universe, from which the resulting gravitational waves could be detectable with the upcoming Laser Interferometer Space Antenna (LISA). The properties of the phase transition and the resulting gravitational wave spectrum are determined by five key parameters: the nucleation temperature $T_n$, phase transition strength at the nucleation temperature $α_n$, bubble wall speed $v_\text{wall}$, transition rate $β$ and the sound speed $c_s$. Of these, the sound speed $c_s$ is determined by the equation of state $p(T,φ)$. In most studies, the plasma of the early universe has been assumed to be ultrarelativistic and therefore following the bag equation of state with $c_s = \frac{1}{\sqrt{3}}$. In this thesis, the PTtools simulation framework for first-order phase transitions, based on the Sound Shell Model, has been extended to include support for arbitrary equations of state and therefore for a temperature- and phase-dependent sound speed $c_s(T,φ)$. The thesis also functions as a reference manual for PTtools. The framework has been tested with the constant sound speed model, in which the sound speed is a different constant in each phase. The sound speed has been shown to have a significant effect on the resulting gravitational wave spectrum, especially when changing the sound speed results in a change in the type of the solution. This has laid the groundwork for simulating cosmological phase transitions with realistic equations of state. This will result in in gravitational wave spectra that can be used in the LISA data analysis pipeline to search for the existence and parameters of a first-order phase transition in the early universe.

Figures (8)

• Figure 1: The thermal effective potential at different temperatures. Generated with PTtools utilities. See also lecture_notes.
• Figure 2: Relation between the fluid velocity just ahead of the wall $\tilde{v}_+$ and just behind the wall $\tilde{v}_-$. Generated with PTtools. See also lecture_notes.
• Figure 3: Three different types of relativistic combustion. Generated with PTtools. See also lecture_notes[fig. 14]mazumdar_review_2019.
• Figure 4: Self-similar fluid profiles with four sound speed combinations, three different wall speeds $v_\text{wall}$ and two transition strengths $\alpha_n$
• Figure 5: Gravitational wave power spectra computed with the sound shell model from the fluid profiles of fig. \ref{['fig:fluid_profiles']}