Tests of general relativity with Einstein Telescope

Gravitational wave signals from compact binary coalescences provide powerful and reliable probes of General Relativity. To date, the LIGO-Virgo-KAGRA collaboration has provided stringent consistency tests of General Relativity predictions. In this work, we present forecasts for how accurately General Relativity can be tested using third-generation ground-based interferometers, focusing on Einstein Telescope (ET) and binary black hole mergers. Given the expected high detection rate, we use a Fisher matrix approach to simulate parameter estimation over large source catalogs, and jointly analyze events within a Bayesian hierarchical framework. We compare different ET configurations and forecast constraints on parametrized deviations of the inspiral post-Newtonian coefficients. Our results indicate that, within about four months of observations, ET could improve current LVK GWTC-3 bounds by roughly four orders of magnitude for the dipole radiation term and about two orders for higher-order coefficients. We further assess the number of detections required to confidently identify deviations from General Relativity at various post-Newtonian orders and for different detector configurations.