# Gravitational wave observations, distance measurement uncertainties, and cosmology

## TL;DR

This paper derives analytical formulas for estimating the uncertainties in gravitational wave-based distance measurements, highlighting how detector configurations and source positions affect the accuracy of cosmological parameter inference.

## Contribution

It provides new analytic expressions for statistical errors in gravitational wave distance measurements, accounting for detector network and source sky position degeneracies.

## Key findings

- Analytic error estimates agree with Bayesian simulations.
- Certain detector configurations hinder distance estimation.
- Implications for Hubble constant measurement accuracy.

## Abstract

Gravitational waves from the coalescence of compact binaries, together with an associated electromagnetic counterpart, are ideal probes of cosmological models. As demonstrated with GW170817, such multimessenger observations allow one to use the source as a standard siren, analog of standard candles in conventional astronomy, in order to measure cosmological parameters such as the Hubble constant. No cosmological ladder is needed to estimate the source luminosity distance from the detected gravitational waves. The error on the luminosity distance plays a crucial r\^ole in the error budget for the inference of the Hubble constant. In this paper, we provide analytic expressions for the statistical errors on the luminosity distance inferred from gravitational wave data as a function of the sky position and the detector network. In particular, we take into account degeneracy in the parameter space of the gravitational waveform showing that in certain conditions on the gravitational-wave detector network and the source sky position it may not be possible to estimate the luminosity distance of the source. Our analytic approximants shows a good agreement with the uncertainties measured with Bayesian samplers and simulated data. We also present implications for the estimation error on the Hubble constant.