Tests of General Relativity with Einstein Telescope

TL;DR

This paper forecasts how third-generation gravitational wave detectors like the Einstein Telescope can test General Relativity with high precision, using a Fisher matrix approach to analyze large binary black hole populations efficiently.

Contribution

It introduces a Fisher matrix-based method for forecasting GR tests with Einstein Telescope, enabling analysis of large event populations without full Bayesian computations.

Findings

ET could measure dipole radiation at $ ext{O}(10^{-7})$ accuracy.

ET could constrain higher-order post-Newtonian coefficients to $ ext{O}(10^{-3})$.

Number of detections needed to identify deviations depends on detector configuration.

Abstract

Gravitational wave signals from compact binary coalescences offer a powerful and reliable probe 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 the accuracy with which 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, performing full Bayesian analyses for each event becomes computationally challenging. To overcome this, we adopt a Fisher matrix approach, simulating parameter estimation in an idealized observation scenario, which allows us to study large populations of compact binary coalescences with feasible computational efforts. Within this framework, we investigate the constraints that ET, in its different configurations, can impose on inspiral post-Newtonian coefficients, by jointly analyzing events using a Bayesian hierarchical methodology. Our results indicate that ET could in principle achieve an accuracy of $\mathcal{O}(10^{-7})$ on the dipole radiation term and $\mathcal{O}(10^{-3})$ on higher-order post-Newtonian coefficients, for both the triangular and the two L-shaped designs, with $10^4$ catalog events. We also assess the number of detections required to confidently identify deviations from General Relativity at various post-Newtonian orders and for different detector configurations.