Precision standard siren cosmology

We discuss the constraints on the Hubble constant to be expected from standard siren sources in ground-based gravitational wave detectors. We consider binary neutron star and binary black hole sources, and focus on the role of golden sirens (the loudest and best constrained sources) to constrain cosmological parameters. We consider two approaches: the counterpart case, where electromagnetic observations provide an independent measurement of the redshift to the sources, and the statistical case, incorporating an analysis over all potential host galaxies within the localization volumes. Our analysis includes realistic measurement uncertainties and selection biases. Although the specific results depend on the configuration and sensitivity of the detector networks, we find that the statistical method would constrain $H_0$ to $4\%$ with $\sim100$ detections of binary neutron star mergers, while an equivalent statistical measurement can be accomplished with $\sim30$ golden events (all fractional uncertainties are quoted as half of the width of the symmetric 68% credible interval divided by the median of the $H_0$ posterior). Alternatively, with $\sim10/60/200$ binary neutron star standard sirens with electromagnetic counterparts, $H_0$ would be constrained to $4/2/1\%$. Given current rate uncertainties, the 5% measurement may happen within the 9 month O3 LIGO/Virgo run (starting Fall 2018), or if the rate is low this may not happen until one full year of the LIGO/Virgo network at design sensitivity (starting $\sim$2021+). Similarly, the 1% measurement may happen within two years of running at design sensitivity ($\sim$2024+), or may not happen until 3+ years of operation of a full five-detector network. Although the rates, and thus precise timetable, remain uncertain, precision standard siren cosmology can be expected in the foreseeable future.