Linear anisotropies in dispersion-measure-based cosmological observables

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