Pure gravitational wave estimation of Hubble’s constant using neutron star–black hole mergers

It has been predicted before the first detection of such events by LIGO (Laser Interferometer Gravitational-Wave Observatory) that the gravitational wave (GW) emission from compact binary coalescence can be used to constrain the expansion rate of the Universe. Here we show how $H_0$ can be derived purely from the GW of neutron star–black hole (NSBH) mergers using a Bayesian hierarchical inference framework. This method provides an estimate of $H_0$ spanning the redshift range $z<0.25$ with current GW sensitivity and without the need for any afterglow detection. We utilize the inherent distribution of neutron star masses together with the NSBH waveform amplitude and frequency to estimate distance and redshift, respectively, thereby measuring $H_0$ for the NSBH events up to systematics and observational uncertainties. With the most updated observations, our first estimate is $H_0 = 96^{+44}_{-50}$ km s−1 Mpc−1 for the likely NSBH events GW190426 and GW200115 using the proof-of-concept analysis outlined in this work. Taking into account of realistic detectors response and sensitivity, we forecast that soon, with 10 more such NSBH events, we can reach competitive precision of $\delta H_0/H_0 \lesssim 20 {{\, \rm per \, cent}}$. It is valuable to have a completely independent, both in terms of observations and relevant physics, method of determining $H_0$ as is emphasized by the current controversy on $H_0$ and attempts to explain it by invoking new physics.