Recovering SGWBs in simulated LISA data with non-stationary components

First-order phase transitions in the early universe are predicted by many Standard Model extensions. They could create a stochastic gravitational wave background (SGWB) observable in the millihertz range, the peak sensitivity range of the next-generation spaceborne observatory LISA. However, possible phase transition signals will be buried under instrument noises and a foreground signal from millions of galactic binary systems. Cosmological SGWBs are isotropic and produce stationary signals in LISA, while the noise components have various non-stationarities, including the annual modulation of the galactic foreground, time evolution of the test-mass noise, and data gaps of varying lengths. Here we explore methods to overcome these challenges, and see that in some cases the non-stationarities may also be useful in distinguishing between the signal and the noise.