Are the distributions of fast radio burst properties consistent with a cosmological population?

High time resolution radio surveys over the last few years have discovered a population of millisecond-duration transient bursts called fast radio bursts (FRBs), which remain of unknown origin. FRBs exhibit dispersion consistent with propagation through a cold plasma and dispersion measures indicative of an origin at cosmological distances. In this paper, we perform Monte Carlo simulations of a cosmological population of FRBs, based on assumptions consistent with observations of their energy distribution, their spatial density as a function of redshift and the properties of the interstellar and intergalactic media. We examine whether the dispersion measures, fluences, derived redshifts, signal-to-noise ratios and effective widths of known FRBs are consistent with a cosmological population. Statistical analyses indicate that at least 50 events at Parkes are required to distinguish between a constant comoving FRB density, and an FRB density that evolves with redshift like the cosmological star formation rate density.