Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis

TL;DR

This paper develops a higher-order asymptotic analysis method to estimate errors in gravitational wave parameter measurements, aiming to detect deviations from General Relativity in binary inspiral signals.

Contribution

It introduces an improved error estimation technique based on higher-order asymptotic expansions for gravitational wave data analysis, enabling better constraints on GR violations.

Findings

Potential to constrain deviations from GR at SNR of 15-17

Errors on ppE parameters affect estimates of mass parameters

Method improves upon the classical Cramér-Rao Lower Bound

Abstract

A frequentist asymptotic expansion method for error estimation is employed for a network of gravitational wave detectors to assess the amount of information that can be extracted from gravitational wave observations. Mathematically we derive lower bounds in the errors that any parameter estimator will have in the absence of prior knowledge to distinguish between the post-Einsteinian (ppE) description of coalescing binary systems and that of general relativity. When such errors are smaller than the parameter value, there is possibility to detect these violations from GR. A parameter space with inclusion of dominant dephasing ppE parameters $(\beta, b)$ is used for a study of first- and second-order (co)variance expansions, focusing on the inspiral stage of a nonspinning binary system of zero eccentricity detectible through Adv. LIGO and Adv. Virgo. Our procedure is an improvement of the Cram\'{e}r-Rao Lower Bound. When Bayesian errors are lower than our bound it means that they depend critically on the priors. The analysis indicates the possibility of constraining deviations from GR in inspiral SNR ($\rho \sim 15-17$) regimes that are achievable in upcoming scientific runs (GW150914 had an inspiral SNR $\sim 12$). The errors on $\beta$ also increase errors of other parameters such as the chirp mass $\mathcal{M}$ and symmetric mass ratio $\eta$. Application is done to existing alternative theories of gravity, which include modified dispersion relation of the waveform, non-spinning models of quadratic modified gravity, and dipole gravitational radiation (i.e., Brans-Dicke type) modifications.