Linear anisotropies in dispersion-measure-based cosmological observables

TL;DR

This paper derives the linear-order contributions to dispersion measure fluctuations in cosmology, assesses their observational relevance, and finds that electron density fluctuations dominate the signal over relativistic effects and lensing.

Contribution

It provides a comprehensive derivation of all linear-order contributions to dispersion measure fluctuations, including relativistic effects, and evaluates their significance for cosmological observations.

Findings

Relativistic effects are negligible for current and future fast radio burst observations.

Electron density fluctuations dominate the dispersion measure clustering signal.

Relativistic effects are re-derived using the geodesic equation in a perturbed metric.

Abstract

We derive all contributions to the dispersion measure (DM) of electromagnetic pulses to linear order in cosmological perturbations, including both density fluctuations and relativistic effects. We then use this result to calculate the power spectrum of DM-based cosmological observables to linear order in perturbations. In particular, we study two cases: maps of the dispersion measure from a set of localized sources (including the effects of source clustering), and fluctuations in the density of DM-selected sources. The impact of most relativistic effects is limited to large angular scales, and is negligible for all practical applications in the context of ongoing and envisaged observational programs targeting fast radio bursts. We compare the leading contributions to DM-space clustering, including the effects of gravitational lensing, and find that the signal is dominated by the fluctuations in the free electron column density, rather than the local source clustering or lensing contributions. To compensate for the disappointing irrelevance of relativistic effects, we re-derive them in terms of the geodesic equation for massive particles in a perturbed Friedmann-Robertson-Walker metric.