  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.
