Cosmological Covariance of Fast Radio Burst Dispersions

TL;DR

This paper investigates the covariance of FRB dispersion measures caused by large-scale structure, deriving analytical models to improve cosmological parameter estimation from future large samples of FRBs with known redshifts.

Contribution

It introduces an analytical framework for the covariance matrix of FRB dispersion measures, highlighting its importance for unbiased cosmological inference with large FRB samples.

Findings

Covariance significantly impacts parameter estimation for over 300 FRBs.

Ignoring covariance leads to overly optimistic constraints.

The method applies also to Gamma Ray Burst afterglows.

Abstract

The dispersion of fast radio bursts (FRBs) is a measure of the large-scale electron distribution. It enables measurements of cosmological parameters, especially of the expansion rate and the cosmic baryon fraction. The number of events is expected to increase dramatically over the coming years, and of particular interest are bursts with identified host galaxy and therefore redshift information. In this paper, we explore the covariance matrix of the dispersion measure (DM) of FRBs induced by the large-scale structure, as bursts from a similar direction on the sky are correlated by long wavelength modes of the electron distribution. We derive analytical expressions for the covariance matrix and examine the impact on parameter estimation from the FRB dispersion measure - redshift relation. The covariance also contains additional information that is missed by analysing the events individually. For future samples containing over $\sim300$ FRBs with host identification over the full sky, the covariance needs to be taken into account for unbiased inference, and the effect increases dramatically for smaller patches of the sky. Also forecasts must consider these effects as they would yield too optimistic parameter constraints. Our procedure can also be applied to the DM of the afterglow of Gamma Ray Bursts.