Reconstruction of Baryon Fraction in Intergalactic Medium through Dispersion Measurements of Fast Radio Bursts

Fast radio bursts (FRBs) probe the total column density of free electrons in the intergalactic medium (IGM) along the path of propagation though the dispersion measures (DMs) which depend on the baryon mass fraction in the IGM, i.e., $f_{\rm IGM}$. In this letter, we investigate the large-scale clustering information of DMs to study the evolution of $f_{\rm IGM}$. When combining with the Planck 2018 measurements, we could give tight constraints on the evolution of $f_{\rm IGM}(z)$ from about $10^4$ FRBs with the intrinsic DM scatter of $30(1+z)~ \rm pc/cm^3$ spanning 80% of the sky and redshift range $z=0-3$. Firstly, we consider the Taylor expansion of $f_{\rm IGM}(z)$ up to second order, and find that the mean relative standard deviation $\sigma(f_{\rm IGM})\equiv\left\langle \sigma[f_{\rm IGM}(z)] /f_{\rm IGM}(z) \right\rangle$ is about 7.2%. In order to alleviate the dependence on fiducial model, we also adopt a non-parametric methods in this work, the local principle component analysis. We obtain the consistent, but weaker constraints on the evolution of $f_{\rm IGM}(z)$, namely the mean relative standard deviation $\sigma(f_{\rm IGM})$ is 24.2%. With the forthcoming surveys, this could be a complimentary method to investigate the baryon mass fraction in the IGM.