Probing modified gravitational wave propagation with strongly lensed coalescing binaries

It has been recently shown that quadruply lensed gravitational-wave (GW) events due to coalescing binaries can be localized to one or just a few galaxies, even in the absence of an electromagnetic counterpart. We discuss how this can be used to extract information on modified GW propagation, which is a crucial signature of modifications of gravity at cosmological scales. We show that, using quadruply lensed systems, it is possible to constrain the parameter Ξ0 that characterizes modified GW propagation, without the need of imposing a prior on H0. A LIGO/Virgo/Kagra network at target sensitivity might already get a significant measurement of Ξ0, while a third-generation GW detector such as the Einstein Telescope could reach a very interesting accuracy.