General Relativity (GR) has been extensively tested in different regimes, particularly under weak gravity, low relative speeds, and linear conditions, but also in strong-field and very low-speed scenarios. The groundbreaking discovery of Gravitational Wave (GW) astronomy in the past decade has significantly advanced our understanding of the gravitational interaction in extreme gravity environments. One of the key scientific goals of future ground-based GW detectors like the Einstein Telescope (ET) is to test Einstein’s theory of GR and explore the nature of GW sources, such as compact objects; holding extraordinary potential for breakthroughs in astrophysics, cosmology, and fundamental physics.
This work mainly focuses on a test of gravity in the extreme regime, more precisely on a forecast for model-agnostic deviations to the inspiral phase of the GW signal emitted by compact binary coalescing systems as predicted by GR. Several Parameter Estimation (PE) codes, tuned toward future detectors, are based on the Fisher information matrix formalism. An important goal of this project is to exploit and generalize GWFish, a simulation software designed to investigate the PE capabilities of different GW networks of detectors, to evaluate statistical constraints expected from ET on possible modifications to GR.
Beginning with state-of-art GR templates like TaylorF2 and IMRPhenomD, we explore two types of potential deviations from the Post-Newtonian (PN) coefficients of the early inspiral phase of the GW simulated signal: Parametrized-post-Einstenian corrections and model-agnostic deviations from the multipolar structure and tidal properties of a Kerr black hole. We provide statistical constraints, obtained through single-event simulations, on single modifications as functions of the PN order at which they enter. By leveraging GWFish flexibility in detector-network simulations, we explore how the predicted constraints from ET could improve by roughly an order of magnitude compared to current and even anticipated future interferometers, such as Advanced LIGO in its fifth observing run. Additionally, To ensure confidence in our results, we compare them to a parallel full Bayesian analysis performed with Bilby, and we investigate the ET capability of breaking correlations among parameters, or parametrized deviations, entering the GW phase.