On tests of general relativity with binary radio pulsars

TL;DR

This paper introduces a Bayesian method for testing general relativity with binary radio pulsars, offering more accurate and comprehensive model comparisons than traditional least-square-fit approaches.

Contribution

It develops a Bayesian framework that accounts for the likelihood structure, compares models via evidence ratios, and combines data from multiple systems for robust tests of gravity theories.

Findings

The Bayesian approach outperforms traditional methods in model comparison.

Simulated data demonstrate the method's effectiveness with current observations.

Joint analysis of multiple pulsar systems enhances testing power.

Abstract

The timing of radio pulsars in binary systems provides a superb testing ground of general relativity. Here we propose a Bayesian approach to carry out these tests, and a relevant efficient numerical implementation, that has several conceptual and practical advantages with respect to traditional methods based on least-square-fits that have been used so far: (i) it accounts for the actual structure of the likelihood function - and it is not predicated on the Laplace approximation which is implicitly built in least-square fits that can potentially bias the inference - (ii) it provides the ratio of the evidences of any two models under consideration as the statistical quantity to compare different theories, and (iii) it allows us to put joint constraints from the monitoring of multiple systems, that can be expressed in terms of ratio of evidences or probability intervals of global (thus not system-dependent) parameters of the theory, if any exists. Our proposed approach optimally exploits the progress in timing of radio pulsars and the increase in the number of observed systems. We demonstrate the power of this framework using simulated data sets that are representative of current observations.