Gravitational-Wave Microlensing as a Probe of Compact Object Population

The abundance of compact objects ranging from stellar to intermediate masses (~ 1 - 10⁵M_) remains poorly constrained, particularly for populations such as primordial black holes and dark matter subhalos that emit little or no electromagnetic radiation. Gravitational-wave (GW) microlensing provides a complementary way to probe these populations through wave-optics effects imprinted on the GW signals, with implications for astrophysical and cosmological inference. We develop a hierarchical Bayesian framework to infer the population properties of microlenses from an ensemble of microlensed GW events, constraining the slope of the power-law lens mass function (αML), the lens number density (n₀), and the fraction of dark matter in compact lenses (fDM). Using simulated microlensed GW signals drawn from a realistic binary black hole population, we find that ~ 100 detected microlensed events are able to constrain both αML and n₀, although a degeneracy between the two remains. For a low-mass-dominated lens population (αML=2) with n₀=10⁶~Mpc⁻³, a three-year observation at the O4 sensitivity yields ~ 130 detectable microlensed events and recovers the injected dark-matter fraction, fDM 1.2 × 10⁻⁴, with a 90% credible interval of 7.3 × 10⁻⁵ fDM 1.8 × 10⁻⁴.