Mounting evidence suggests that planned and present gravitational-wave detectors may be sensitive to signatures from first-order phase transitions in the early universe. These events, potentially present in the primordial universe, create a broad spectrum of GWs, the stochastic remnants of which could then be observed in the various next-generation experiments. The aim of this internship is to explore the presence, strength, and finally possible GW signatures of first order transitions in new physics models with supplementary gauge groups motivated by the Standard Model flavour problems – so-called horizontal gauge groups. The calculation of the finite temperature effective potential of the flavour model will be performed using the effective Lagrangian reduction method implemented in the code DRalgo and further used to study and model the phase transition as well as modelling GW behaviour in the wake of a first-order phase transition. For interested candidates with experience in coding, programming-intensive directions could also include further developing a relativistic hydrodynamics of the dynamics of a phase transition and the Bayesian analysis of subsequent emission of GWs. Interactions with the experimental GWs group at IP2I is expected. This internship may be continued by a PhD project pending to obtaining a PhD funding from the Doctoral School.