Uncertainty and bias of cosmology and astrophysical population model from statistical dark sirens

TL;DR

This paper derives the theoretical limits on the accuracy of cosmological and astrophysical parameter estimation using gravitational-wave dark sirens, highlighting how model inaccuracies can bias results, especially with large event samples.

Contribution

It provides analytical Fisher information bounds for dark siren cosmology and investigates the impact of unmodeled substructures on bias and accuracy.

Findings

A 1% deviation in astrophysical models can cause over 1% bias in Hubble constant estimation.

The method enables fast, accurate estimation of statistical errors in dark siren cosmology.

Bias becomes significant with more than 10,000 BBH events detected.

Abstract

Gravitational-wave (GW) radiation from a coalescing compact binary is a standard siren as the luminosity distance of each event can be directly measured from the amplitude of the signal. One possibility to constrain cosmology using the GW siren is to perform statistical inference on a population of binary black hole (BBH) events. In essence, this statistical method can be viewed as follows. We can modify the shape of the distribution of observed BBH events by changing cosmological parameters until it eventually matches the distribution constructed from an astrophysical population model, thereby allowing us to determine the cosmological parameters. In this work, we derive the Cram\'er-Rao bound for both cosmological parameters and those governing the astrophysical population model from this statistical dark siren method by examining the Fisher information contained in the event distribution. Our study provides analytical insights and enables fast yet accurate estimations of the statistical accuracy of dark siren cosmology. Furthermore, we consider the bias in cosmology due to unmodeled substructures in the merger rate and the mass distribution. We find a $1\%$ deviation in the astrophysical model can lead to a more than $1\%$ error in the Hubble constant. This could limit the accuracy of dark siren cosmology when there are more than $10^4$ BBH events detected.