Constraining the lensing of binary neutron stars from their stochastic background

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 nondetection of a stochastic GW background. Following closely the formalism we developed previously [R. Buscicchio et al., Phys. Rev. Lett. 125, 141102 (2020)., 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 μ >1.02 is less than ∼7 ×10-8 and therefore such events should not be expected in the near future. We also make predictions for projected future sensitivities.