On Dark Gravitational Wave Standard Sirens as Cosmological Inference and Forecasting the Constraint on Hubble Constant using Binary Black Holes Detected by Deci-hertz Observatory

TL;DR

This paper explores using dark gravitational wave standard sirens from binary black hole mergers detected by the Deci-hertz Observatory to precisely measure the Hubble constant, even without electromagnetic counterparts, by combining GW data with galaxy surveys.

Contribution

It demonstrates the potential of dark sirens for cosmology, introduces bias correction methods, and forecasts the Hubble constant constraints achievable with upcoming GW observations.

Findings

Hubble constant can be constrained to <1% accuracy with tens of BBH mergers.

Deci-hertz Observatory may detect ~100 BBHs in half a year, enabling ~0.1-1% Hubble constant measurement.

Bias correction methods are effective for moderate errors in luminosity distance and localization.

Abstract

Gravitational wave (GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if their redshift can be measured independently. However, mergers of stellar binary black holes (BBHs) may not have electromagnetic counterparts and thus have no direct redshift measurements. These dark sirens may be still used to statistically constrain cosmological parameters by combining their GW measured luminosity distances and localization with deep redshift surveys of galaxies around it. We investigate this dark siren method in detail by using mock BBH and galaxy samples. We find that the Hubble constant can be constrained well with an accuracy $\lesssim1\%$ with a few tens or more of BBH mergers at redshift up to $1$ if GW observations can provide accurate estimates of their luminosity distance (with relative error of $\lesssim0.01$) and localization ($\lesssim0.1~\rm{deg}^2$), though the constraint may be significantly biased if the luminosity distance and localization errors are larger. We also introduce a simple method to correct this bias and find it is valid when the luminosity distance and localization errors are modestly large. We further generate mock BBH samples, according to current constraints on BBH merger rate and the distributions of BBH properties, and find that the Deci-hertz Observatory (DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio $\varrho\gtrsim30$, relative luminosity distance error $\lesssim0.02$, and localization error $\lesssim0.01\rm{deg}^2$. By applying the dark standard siren method, we find that the Hubble constant can be constrained to the $\sim0.1-1\%$ level using these DO BBHs, an accuracy comparable to the constraints obtained by using electromagnetic observations in the near future, thus it may provide insight into the Hubble tension.