Multi-spectral Sirens: Gravitational-wave Cosmology with (Multi-) Sub-populations of Binary Black Holes

The cosmic expansion rate can be directly measured with gravitational-wave (GW) data of the compact binary mergers by jointly constraining the mass function of the population and the cosmological model via the so-called spectral sirens. Such a method relies on the features in the mass functions, which may originate from some individual subpopulations, and hence become blurred/indistinct due to the superposition of different subpopulations. In this work we propose a novel approach to constrain the cosmic expansion rate with subpopulations of GW events, named multi-spectral sirens. The advantage of the multi-spectral sirens compared to the traditional spectral sirens is demonstrated by the simulation with the mock data. The application of this approach to the GWTC-3 data yields $H_0=73.3_{-25.6}^{+29.9}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ (median and symmetric 68.3% credible interval), which is about 19% tighter than the result inferred with the traditional spectral sirens utilizing a PowerLaw+Peak mass function. The incorporation of the bright standard siren GW170817 with a uniform prior in [10,200] (log-uniform prior in [20,140]) ${\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ gives $H_0=71.1_{-7.5}^{+15.0}(70.3_{-7.1}^{+12.9}){\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ (68.3% confidence level), corresponding to an improvement of $\sim 26\mathrm{\%}$ (23%) with respect to the measurement from sole GW170817.