FRB cosmology with the RM-PRS Luminosity Correlation

Fast Radio Bursts (FRBs) have emerged as a powerful tool for cosmological studies, particularly through the dispersion measure-redshift ($\mathrm{DM}-z$) relation. This work proposes a novel calibration method for FRBs using the Yang-Li-Zhang (YLZ) empirical relation, which links the rotation measure (RM) of FRBs to the luminosity of their associated persistent radio sources (PRS). We demonstrate that this approach provides independent constraints on cosmological parameters, bypassing limitations inherent to traditional $\mathrm{DM}-z$ method. Utilizing the current sample of four YLZ-calibrated FRBs, we derive a Hubble constant measurement of $H_0 = 86.18_{-14.99}^{+18.03}\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$ (68\% CL). Monte Carlo simulations indicate that a future catalog of 400 FRB-PSR systems could reduce the relative uncertainty of $H_0$ to 4.5\%. Combining YLZ-calibrated FRBs with $\mathrm{DM}-z$ sample reveals critical synergies: joint analysis of equalized samples ($N=100$ for both methods) reduces the relative uncertainty of $H_0$ to 2.9\%, mainly because the incorporation of PRS observations substantially mitigates the degeneracy between the parameters such as IGM baryon mass fraction ($f_{\rm IGM}$) and other cosmological parameters inherent to the $\mathrm{DM}-z$ relation.