Assessing the impact of unequal noises and foreground modeling on SGWB reconstruction with LISA

In the search for stochastic gravitational wave backgrounds (SGWB) of cosmological origin with LISA, it is crucial to account for realistic complications in the noise and astrophysical foreground modeling that may impact the signal reconstruction. To address these challenges, we updated the SGWBinner code to incorporate both variable noise levels across LISA arms and more complex foreground spectral shapes. We extended previous studies, which assumed only two parameters for both noise and foregrounds, simulating SGWB searches with up to 12 and 8 parameters for noise and foregrounds, respectively. To perform this more challenging analysis, we have integrated the JAX framework into the SGWBinner code, which significantly improves its computational efficiency and enables faster Bayesian likelihood sampling and more effective exploration of complex models. We found that whereas increased noise complexity leads to only a tens-of-percent increase in the reconstruction error, the complexity of foregrounds can degrade the constraints by up to one order-of-magnitude depending on the assumptions. Our findings suggest that, while moderate variations in noise amplitudes have a minimal impact, poor foreground modeling (i.e., templates requiring many free parameters) significantly degrades the reconstruction of cosmological signals. This underlines the importance of accurate modeling and subtraction of astrophysical foregrounds to characterize possible cosmological components.