Reconstructing the Fraction of Baryons in the Intergalactic Medium with Fast Radio Bursts via Gaussian Processes

Fast radio bursts (FRBs) are a promising new probe for astronomy and cosmology. Thanks to their extragalactic and cosmological origin, FRBs could be used to study the intergalactic medium (IGM) and the cosmic expansion. It is expected that numerous FRBs with identified redshifts will be available in the near future through the identification of their host galaxies or counterparts. $\rm DM_{IGM}$, the contribution from IGM to the observed dispersion measure (DM) of FRB, carries the key information about IGM and the cosmic expansion history. We can thus study the evolution of the universe by using FRBs with identified redshifts. In the present work, we are interested in the fraction of baryon mass in the IGM, $f_{\rm IGM}$, which is useful to study the cosmic expansion and the problem of the "missing baryons". We propose to reconstruct the evolution of $f_{\rm IGM}$ as a function of redshift $z$ with FRBs via a completely model-independent method, namely Gaussian processes. Since there is not a large sample of FRBs with identified redshifts, we use simulated FRBs instead. Through various simulations, we show that this methodology works well.