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 $H_0=73.3^{+29.9}_{-25.6}~{\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ (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]) ${\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ gives $H_0=71.1^{+15.0}_{-7.5}~(70.3^{+12.9}_{-7.1})~{\rm Mpc}^{-1}~{\rm km}~{\rm s}^{-1}$ (68.3\% confidence level), corresponding to an improvement of $\sim26\%$ (23\%) with respect to the measurement from sole GW170817.