Constraining the Evolution of the Baryon Fraction in the IGM with FRB and H(z) data

Extragalactic dispersion measures (DMs) obtained from observations of fast radio bursts (FRBs) are an excellent tool for probing intergalactic medium (IGM) and for conducting cosmography. However, the DM contribution from the IGM (${\rm DM_{IGM}}$) depends on the fraction of baryon mass in the IGM, $f_{\rm IGM}$, which is not properly constrained. As $f_{\rm IGM}(z)$ is geometrically related to the Hubble parameter $H(z)$ and ${\rm DM_{IGM}}(z)$, here we propose that combining two independent measurements of FRBs and $H(z)$ in similar redshift ranges provides a novel and cosmology-free method to constrain the evolution of $f_{\rm IGM}(z)$. Under the assumption that $f_{\rm IGM}$ is evolving with redshift in a functional form, we forecast that the evolution of $f_{\rm IGM}(z)$ can be well inferred in a combined analysis of $\sim3000$ ${\rm DM_{IGM}}(z)$ derived from FRBs and $\sim50$ $H(z)$ derived from the Hubble parameter data. Though the efficiency of our method is not as good as that of the other model-independent method involving the joint measurements of DM and luminosity distance of FRBs, our method offers a new model-independent way to constrain $f_{\rm IGM}(z)$.