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 $\mathtt{\text{SGWBinner}}$ code to incorporate both variable noise levels across LISA arms and more complex foreground spectral shapes. Our findings suggest that, while moderate variations of the 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 the astrophysical foregrounds to characterize possible cosmological components. To perform this more challenging analysis, we have integrated the $\mathtt{\text{JAX}}$ framework, which significantly improves the computational efficiency of the code, in the $\mathtt{\text{SGWBinner}}$ code, enabling faster Bayesian likelihood sampling and more effective exploration of complex SGWB signals.