Recovering a phase transition signal in simulated LISA data with a modulated galactic foreground

Stochastic backgrounds of gravitational waves from primordial first-order phase transitions are a key probe of physics beyond the Standard Model. They represent one of the best prospects for observing or constraining new physics with the LISA gravitational wave observatory. However, the large foreground population of galactic binaries in the same frequency range represents a challenge, and will hinder the recovery of a stochastic background. To test the recoverability of a stochastic gravitational wave background, we use the LISA Simulation Suite to generate data incorporating both a stochastic background and an annually modulated foreground modelling the galactic binary population, and the Bayesian analysis code Cobaya to attempt to recover the model parameters. By applying the Deviance Information Criterion to compare models with and without a stochastic background we place bounds on the detectability of gravitational waves from first-order phase transitions. By further comparing models with and without the annual modulation, we show that exploiting the modulation improves the goodness-of-fit and gives a modest improvement to the bounds on detectable models.