Inferring the Intermediate-mass Black Hole Number Density from Gravitational-wave Lensing Statistics

The population properties of intermediate mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation supermassive galaxies. Gravitational wave observations can help fill gap from stellar to holes. In our work, we propose new method for probing lens populations through lensing statistics gravitational waves, here focusing on inferring number density Using hierarchical Bayesian inference injected lensed find that existing observatories at design sensitivity either identify an $10^6 \mathrm{Mpc}^{-3}$ or place upper bound $\lesssim 10^4 $10^3 \mathrm{Mpc}^{-3}$. More broadly, be applied probe other forms compact matter as well.