Impact of correlated noise on the reconstruction of the stochastic gravitational wave background with the Einstein Telescope

The Einstein Telescope (ET) is a proposed next-generation gravitational wave (GW) interferometer designed to detect a large number of astrophysical and cosmological sources with unprecedented sensitivity. A key target for ET is the detection of a stochastic gravitational-wave background (SGWB), a faint signal from unresolved GW sources. In its proposed triangular configuration, correlated Newtonian noise of seismic origin poses some challenges for the SGWB detection. We study the impact of correlated noise on the SGWB detection and relative parameter estimation for ET in the triangular configuration, comparing it to a 2L configuration with two separated L-shaped detectors. We perform a Bayesian analysis on simulated data, which shows that accurate reconstruction of the SGWB parameters and instrumental noise is achievable if the noise is properly modeled. We illustrate that neglecting correlated noise leads to significant biases in the parameter reconstruction. Our results show that, while the 2L configuration provides slightly better parameter estimation precision, mainly due to its longer arm length, the triangular configuration remains competitive when accurate noise modeling is provided.