Next-generation ground-based gravitational-wave (GW) detectors are expected to detect millions of binary black hole mergers during their operation period. A small fraction ($\sim 0.1–1\%$) of them will be strongly lensed by intervening galaxies and clusters, producing multiple copies of the GW signals. The expected number of lensed events and the distribution of the time delay between lensed images will depend on the mass distribution of the lenses at different redshifts. Warm dark matter and fuzzy dark matter models predict lower abundances of low-mass dark matter halos as compared to the standard cold dark matter. This will result in a reduction in the number of strongly lensed GW events, especially with small time delays. Using the number of lensed events and the lensing time delay distribution, we will be able to put a lower bound on the mass of the warm and fuzzy dark matter particles from a catalog of lensed GW events. Our first forecasts suggest that the expected bounds from GW strong lensing from next-generation detectors are better than the current constraints.

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• Dark matter
• Gravitational lenses
• Gravitational waves
• Particle dark matter