Impact of overlapping signals on parameterized post-Newtonian coefficients in tests of gravity

TL;DR

This paper studies how overlapping gravitational wave signals in next-generation detectors can bias tests of general relativity, especially affecting post-Newtonian coefficients, and assesses the likelihood and impact of such biases.

Contribution

It analyzes the influence of overlapping signals on parameterized GR tests, quantifies their effects on PN coefficients, and evaluates the risk of false deviations in future gravitational wave observations.

Findings

1PN coefficient is most affected by overlaps.

A significant portion of overlaps can bias PN coefficients.

Collective biases tend to average out, favoring GR.

Abstract

Gravitational waves have been instrumental in providing deep insights into the nature of gravity. Next-generation detectors, such as the Einstein Telescope, are predicted to have a higher detection rate given the increased sensitivity and lower cut-off frequency. However, this increased sensitivity raises challenges concerning parameter estimation due to the foreseeable overlap of signals from multiple sources. Overlapping signals (OSs), if not properly identified, may introduce biases in estimating post-Newtonian (PN) coefficients in parameterized tests of general relativity (GR). We investigate how OSs affect $-1$PN to 2PN terms in parameterized GR tests, examining their potential to falsely suggest GR deviations. We estimate the prevalence of such misleading signals in next-generation detectors, and their collective influence on GR tests. We compare the effects of OSs on coefficients at different PN orders, concluding that overall the 1PN coefficient suffers the most. Our findings also reveal that while a non-negligible portion of OSs exhibit biases in PN coefficients that might individually prefer to conclude deviations from GR, collectively, the direction to deviate is random and a statistical combination will still be in favor of GR.