Linear anisotropies in dispersion-measure-based cosmological observables
  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.
