Likelihood for a network of gravitational-wave detectors with correlated noise

The Einstein Telescope faces a critical data analysis challenge with correlated noise, often overlooked in current parameter estimation analyses. We address this issue by presenting the statistical formulation of the likelihood that includes correlated noise for the Einstein Telescope or any detector network. By considering varying degrees of correlation, we probe the impact of noise correlations on the parameter estimation analysis of a GW150914-like event. We show that neglecting these correlations may significantly reduce the accuracy of the chirp mass reconstruction. This emphasizes how critical a proper treatment of correlated noise is, as presented in this work, to unlocking the wealth of results promised by the Einstein Telescope.