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

TL;DR

This paper proposes a novel method combining fast radio burst dispersion data with gravitational wave measurements to break the degeneracy between baryon density and Hubble constant, enabling precise cosmological constraints without early Universe priors.

Contribution

It introduces a Bayesian framework that uses FRBs associated with gravitational wave sources to independently measure cosmological parameters, requiring third-generation GW detectors.

Findings

Forecasts that Einstein Telescope can constrain H_0 to ±6 km/s/Mpc.

Demonstrates that combining dispersion and GW data breaks the baryon-Hubble degeneracy.

Method applicable with other luminosity distance measurements.

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 $\Omega_\mathrm{b}h^2f_\mathrm{d}$ (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 $\Omega_\mathrm{b}h^2f_\mathrm{d}$ to $^{+0.0015}_{-0.0016}$ (68$\,\%$ credible interval). The method can also be used with luminosity distances obtained through other means than GWs.