Cosmological Parameters Estimate from Persistent Radio Sources of Fast Radio Bursts

We introduce a novel method to constrain the Hubble constant ($H_0$) by combining fast radio bursts (FRBs) and their persistent radio sources (PRSs) through the observationally validated Yang relation, $ L_{\nu} \propto | \mathrm{RM} | $, which links PRS luminosity to the rotation measure (RM) of the associated FRB. Using a mock sample of PRSs, we demonstrate that the Yang relation can help to unravel the degeneracies among $H_0$, baryon density parameter $\Omega_b$, and baryon fraction in the intergalactic medium $f_{\mathrm{IGM}}$ in the traditional approach of using dispersion measure only to perform cosmological analyses. Our method employs a two-stage Markov Chain Monte Carlo (MCMC) analysis to constrain $H_0$. Using the available data of six observed PRS systems, we obtain a preliminary constraint of $H_0 = 75 \pm 30~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. We briefly discuss possible refinements of the method by reducing residual degeneracies and systematic uncertainties using future data and physical modeling. Our results indicate that the Yang relation can potentially become a new probe for performing FRB cosmology.