Strong-lensing cosmography using third-generation gravitational-wave detectors

TL;DR

This paper proposes a statistical method to estimate cosmological parameters using strongly lensed binary-black-hole mergers observed by third-generation gravitational-wave detectors, accounting for model biases and contamination effects.

Contribution

It introduces a robust Bayesian framework for cosmological inference from GW lensing data, including bias mitigation and model selection strategies.

Findings

The method achieves high precision in cosmological parameters estimation.

Biases from incorrect redshift or lens models can be mitigated with Bayesian model selection.

Contamination effects can be incorporated without biasing results.

Abstract

We present a detailed exposition of a statistical method for estimating cosmological parameters from the observation of a large number of strongly lensed binary-black-hole (BBH) mergers observable by next (third) generation (XG) gravitational-wave (GW) detectors. This method, first presented in Jana (2023 Phys. Rev. Lett. 130 261401), compares the observed number of strongly lensed GW events and their time delay distribution (between lensed images) with observed events to infer cosmological parameters. We show that the precision of the estimation of the cosmological parameters does not have a strong dependance on the assumed BBH redshift distribution model. Using the large number of unlensed mergers, XG detectors are expected to measure the BBH redshift distribution with sufficient precision for the cosmological inference. However, a biased inference of the BBH redshift distribution will bias the estimation of cosmological parameters. An incorrect model for the distribution of lens properties can also lead to a biased cosmological inference. However, Bayesian model selection can assist in selecting the right model from a set of available parametric models for the lens distribution. We also present a way to incorporate the effect of contamination in the data due to the limited efficiency of lensing identification methods, so that it will not bias the cosmological inference.