[Paper Review] Are Parametrized Tests of General Relativity with Gravitational Waves Robust to Unknown Higher Post-Newtonian Order Effects?

Scott Perkins, Nicolás Yunes|arXiv (Cornell University)|Jan 7, 2022

Pulsars and Gravitational Waves Research81 references43 citations

TL;DR

This paper investigates whether parametrized tests of General Relativity using gravitational waves remain robust when higher post-Newtonian (PN) order corrections are unknown. Using Bayesian parameter estimation on synthetic data, it demonstrates that single-parameter tests are not degraded but actually improved by including higher-order PN terms, provided the mathematical structure of the series is known—offering strong evidence for the robustness of current ppE-based GR tests.

ABSTRACT

Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general relativity (a realization of the parametrized post-Einsteinian framework), where the gravitational waveform, as calculated in Einstein's theory as a series expansion in the orbital velocity, is parametrically deformed at a given set of orders in velocity. However, most current approaches usually only analyze the data while considering a single, specific modification at a time. Are then constraints placed with a single modification robust to our ignorance of higher post-Newtonian order corrections? We show here that for a wide class of theories, specifically those that admit a post-Newtonian expansion, single-parameter tests are indeed robust. In particular, through a series of full Bayesian parameter estimation studies on several different sets of synthetic data, we show that single-parameter constraints are not degraded but rather are improved by the inclusion of multiple parameters, provided one includes information about the mathematical structure of the series. We then exemplify this with a specific theory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where the waveform has been calculated to higher post-Newtonian orders than leading. We show that the inclusion of these higher order terms strengthens single-parameter constraints, instead of weakening them, and that the strengthening is very mild. This analysis therefore provides strong evidence that single-parameter post-Einsteinian tests of general relativity are robust to ignorance of high post-Newtonian order terms in the general relativistic deformations.

Motivation & Objective

• To assess the robustness of single-parameter parametrized post-Einsteinian (ppE) tests of General Relativity against ignorance of higher post-Newtonian (PN) order corrections.
• To determine whether including higher PN terms in waveform models weakens or strengthens constraints on ppE parameters.
• To evaluate whether the inclusion of higher-order PN corrections improves or degrades the precision of single-parameter GR tests.
• To test this robustness in a realistic theory—shift-symmetric scalar Gauss-Bonnet gravity—where higher-order PN corrections are known.
• To provide empirical and theoretical justification for the continued use of single-parameter ppE tests in LIGO/Virgo data analysis.

Proposed method

• Performs full Bayesian parameter estimation on synthetic gravitational wave signals with known ppE deformations.
• Uses waveform models that include both leading-order and higher-order PN corrections in the ppE deformation parameter.
• Applies the parametrized post-Einsteinian (ppE) framework, where deformations are modeled as polynomial terms in orbital velocity with a fixed exponent b and a free amplitude β.
• Compares constraints on β when only the leading-order ppE term is included versus when higher-order terms are also included.
• Employs a specific theory—shift-symmetric scalar Gauss-Bonnet gravity—as a concrete example where higher-order PN corrections are analytically known.
• Uses Markov Chain Monte Carlo (MCMC) sampling with dynamic temperature selection for robust posterior inference.

Experimental results

Research questions

• RQ1 Does the inclusion of higher post-Newtonian (PN) order corrections degrade the precision of single-parameter ppE tests of General Relativity?
• RQ2 Can the inclusion of higher-order PN terms improve the constraints on a single ppE parameter β, even when the true signal contains multiple such terms?
• RQ3 Is the ppE framework robust to ignorance of higher-order PN corrections in the sense that single-parameter tests remain reliable?
• RQ4 How does the inclusion of known higher-order PN terms affect the posterior distribution of β in a realistic modified gravity theory?
• RQ5 To what extent do higher-order PN corrections in the waveform strengthen or weaken single-parameter constraints in parametrized tests?

Key findings

• Single-parameter ppE tests are not degraded but rather improved when higher post-Newtonian (PN) order corrections are included, provided the mathematical structure of the series is known.
• The inclusion of higher-order PN terms leads to a mild but consistent strengthening of constraints on the ppE amplitude coefficient β.
• In the case of shift-symmetric scalar Gauss-Bonnet gravity, where higher-order PN corrections are analytically known, the inclusion of these terms strengthens the constraint on β by a small but measurable amount.
• The improvement in constraint precision is robust across multiple synthetic data sets and different ppE exponents b.
• The results provide strong empirical and theoretical support for the robustness of current LIGO/Virgo parametrized tests of General Relativity.
• The study confirms that single-parameter ppE tests remain a valid and powerful tool for testing GR, even when higher-order PN effects are not fully known in advance.