The curvature dependence of gravitational-wave tests of General Relativity

TL;DR

This paper introduces a universal curvature scaling framework for gravitational-wave tests of General Relativity, enabling theory-agnostic constraints based on the system's mass scale and the order of curvature corrections.

Contribution

It develops a universal, theory-independent method to incorporate curvature dependence into gravitational-wave tests, enhancing the interpretability and scope of deviations from General Relativity.

Findings

Universal curvature scaling relates deviations to system mass and correction order.

The method allows constraints on curvature effects without assuming specific theories.

Application to current gravitational-wave data demonstrates its practical utility.

Abstract

High-energy extensions to General Relativity modify the Einstein-Hilbert action with higher-order curvature corrections and theory-specific coupling constants. The order of these corrections imprints a universal curvature dependence on observations while the coupling constant controls the deviation strength. In this Letter, we leverage the theory-independent expectation that modifications to the action of a given order in spacetime curvature (Riemann tensor and contractions) lead to observational deviations that scale with the system length-scale to a corresponding power. Focusing on gravitational wave observations, the relevant scale is the binary total mass, and deviations scale as a power of mass $p$ related to the action order. For example, $p=4,6$ arise in effective field theory for cubic and quartic theories respectively. We incorporate this universal scaling into theory-agnostic tests of General Relativity with current gravitational-wave observations, thus enabling constraints on the curvature scaling without compromising the agnostic nature of these tests. This introduces a flexible yet highly interpretable new paradigm for tests of General Relativity with gravitational-wave catalogs.