Constraining the lensing of binary neutron stars from their stochastic background

Abstract: Gravitational wave (GW) transients from binary neutron star (BNS) coalescences can, in principle, be subject to gravitational lensing thereby increasing the amplitude and signal-to-noise ratio. We estimate the rate of lensed BNS events resolvable by LIGO and Virgo and find that it is constrained by the current non-detection of a stochastic GW background. Following closely the formalism we developed (10.1103/PhysRevLett.125.141102) in the context of binary black hole lensing, we show that at current sensitivities the fraction of BNS coalescences with lensing magnifications $\mu> 1.02$ is less than $\sim 7\times 10^{-8}$ and therefore such events should not be expected in the near future. We also make predictions for projected future sensitivities.