Accurate Standard Siren Cosmology with Joint Gravitational-Wave and $\gamma$-Ray Burst Observations

TL;DR

This paper presents a method to eliminate bias in standard siren cosmology using joint GW and gamma-ray burst data, enabling unbiased Hubble constant measurement and better understanding of GRB properties.

Contribution

It introduces a new inference scheme that accounts for selection effects directly from multimessenger data, improving cosmological and source property measurements.

Findings

Unbiased Hubble constant measurement achieved.

Method applicable to small-sample data scenarios.

New likelihood approximant for GW events introduced.

Abstract

Joint gravitational-wave (GW) and $\gamma$-ray burst (GRB) observations are among the best prospects for standard siren cosmology. However, the strong selection effect for the coincident GRB detection, which is possible only for sources with small inclination angles, induces a systematic uncertainty that is currently not accounted for. We show that this severe source of bias can be removed by inferring the \emph{a priori} unknown electromagnetic detection probability directly from multimessenger data. This leads at the same time to an unbiased measurement of the Hubble constant, to constrain the properties of GRB emission, and to accurately measure the viewing angle of each source. Our inference scheme is applicable to real data already in the small-statistics regime, a scenario that might become reality in the near future. Additionally, we introduce a novel likelihood approximant for GW events which treats the dependence on distance and inclination as exact.