Probing Dark Matter with Strongly Lensed Binary Black Hole Mergers: Prospects in the Near Future
Gravitational-wave~(GW) transients, strongly lensed by intervening galaxies and clusters, are expected to constitute a small fraction ($\sim 0.1$-$0.5\%$) of the events detectable by ground-based detectors. A strongly lensed binary black hole (BBH) merger will produce multiple copies of the GW signal arriving at different times at the detector. The abundance and time-delay distribution of these lensed events are sensitive to the mass, density profile, and redshift distribution of the lens population, and in turn, to the underlying nature of dark matter. Jana et al. (Phys.Rev.Lett. 135 (2025) 11, 111402) recently proposed a method to constrain the masses of warm dark matter (WDM) particles making use of the strongly lensed events detectable by next-generation GW detectors. In this work, we investigate the prospects of constraining the mass of the WDM particle using upcoming observations of the upgraded LIGO-Virgo-KAGRA network. This requires a careful modeling of the detector selection effects. The upcoming fifth observing run (O5) is expected to yield only a modest bound, since only a few lensed pairs are expected at that early stage. By the sixth observing run (O6), we forecast a bound on the WDM particle mass, $m_{\rm wdm}^{-1} \lesssim 0.1$-$0.2\text{keV}^{-1}$ ($m_{\rm wdm} \gtrsim 5$-$10\text{keV}$), which is comparable to the tightest existing astrophysical constraints. Runs beyond O6 will tighten the constraint by roughly an order of magnitude. Strongly lensed GWs therefore offer a complementary, competitive, and independent probe of dark matter.