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.
