Improved Constraints on Modified Gravity with Eccentric Gravitational Waves

TL;DR

This paper investigates how small orbital eccentricities in gravitational wave signals affect constraints on modified gravity theories, using analytical waveform models and Fisher analysis to forecast future detector sensitivities.

Contribution

It develops analytical waveforms for eccentric inspirals in Jordan-Brans-Dicke-Fierz theory and assesses their impact on constraining the theory with future gravitational wave observations.

Findings

Constraints initially worsen with small eccentricity but improve beyond eccentricity of ~0.03.

Third-generation detectors could tighten constraints by up to an order of magnitude.

Waveform development for eccentric systems in modified gravity is crucial for future physics extraction.

Abstract

Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans- Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular approximation (an expansion in small eccentricity), we first construct an analytical expression for frequency-domain gravitational waveforms produced by inspiraling compact binaries with small eccentricity in this theory. We then calculate the overlap between our approximate analytical waveforms and an eccentric numerical model (TaylorT4) to determine the regime of validity (in eccentricity) of the former. With this at hand, we carry out a Fisher analysis to determine the accuracy to which Jordan-Brans-Dicke-Fierz theory could be constrained given future eccentric detections consistent with General Relativity. We find that the constraint on the theory initially deteriorates (due to covariances between the eccentricity and the Brans-Dicke coupling parameter), but then it begins to recover, once the eccentricity is larger than approximately 0.03. We also find that third-generation ground-based detectors and space-based detectors could allow for constraints that are up to an order of magnitude more stringent than current Solar System bounds. Our results suggest that waveforms in modified gravity for systems with moderate eccentricity should be developed to maximize the theoretical physics that can be extracted in the future.