Constraining the lensing of binary black holes from their stochastic background

TL;DR

This paper links gravitational lensing effects on individual binary black hole signals to the stochastic background, constraining the fraction of resolvable lensed events and clarifying implications for current and future GW observations.

Contribution

It introduces a novel method connecting lensing of GW transients with stochastic background limits, providing new constraints on lensed binary black hole events.

Findings

Lensed binary black hole fraction constrained to less than ~4×10⁻⁵.

Clarifies interpretation of low redshift GW observations in lensing context.

Recent claims of lensed GW events are statistically disfavoured.

Abstract

Gravitational waves (GWs) are subject to gravitational lensing in the same way as electromagnetic radiation. However, to date, no unequivocal observation of a lensed GW transient has been reported. Independently, GW observatories continue to search for the stochastic GW signal which is produced by many transient events at high redshift. We exploit a surprising connection between the lensing of individual transients and limits to the background radiation produced by the unresolved population of binary back hole mergers: we show that it constrains the fraction of individually resolvable lensed binary black holes to less than $\sim 4\times 10^{-5}$ at present sensitivity. We clarify the interpretation of existing, low redshift GW observations (obtained assuming no lensing) in terms of their apparent lensed redshifts and masses and explore constraints from GW observatories at future sensitivity. Based on our results, recent claims of observations of lensed events are statistically disfavoured.