Breaking the Baryon Density$\unicode{x2013}$Hubble Constant Degeneracy in Fast Radio Burst Applications with Associated Gravitational Waves

Abstract

Fast Radio Bursts (FRBs) are a unique probe of the cosmos, owing to dispersion caused by free electrons in the intergalactic medium (IGM). Two of the main quantities of interest are degenerate: the density of matter ${\Omega }_{\mathrm{b}}{f}_{\mathrm{d}}$ outside of galaxies and the Hubble constant $H_0$. Here, we present a new possibility of breaking the degeneracy without invoking early Universe priors on ${\Omega }_{\mathrm{b}}$. Assuming some FRBs originate in compact object mergers, the combination of dispersion and luminosity distance from the gravitational wave (GW) can be used to measure ${\Omega }_{\mathrm{b}}{h}^2{f}_{\mathrm{d}}$ (where $h$ is the dimensionless Hubble constant). We show that this measurement can be combined with the abundant FRBs that have a redshift measurement. This combination breaks the degeneracy with the Hubble constant. We develop a Bayesian framework and forecast that third-generation GW detectors are required to obtain meaningful constraints. We forecast that one year of Einstein Telescope operations can constrain $H_0$ to $\pm 6\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and ${\Omega }_{\mathrm{b}}{h}^2{f}_{\mathrm{d}}$ to ${}_{-0.0016}^{+0.0015}$ (68$\%$ credible interval). The method can also be used with luminosity distances obtained through other means than GWs.

arXiv comment10 pages, 4 figures, 2 tables; submitted to Phys. Rev. D, comments welcome