Cosmological inference using gravitational wave standard sirens: A mock data analysis

International audienceThe observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant H0 using gravitational wave standard sirens. When no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate H0 using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of H0. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of H0, as well as the effect of weighting each galaxy’s likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4% measurement precision can be reached using galaxy catalogs with 50% completeness and ∼250 binary neutron star detections with sensitivity similar to that of Advanced LIGO’s second observing run