Cosmological model-independent constraints on the baryon fraction in the IGM from fast radio bursts and supernovae data

Fast Radio Bursts (FRBs) are millisecond-duration radio transients with an observed dispersion measure ($DM$) greater than the expected Milky Way contribution, which suggests that such events are of extragalactic origin. Although some models have been proposed to explain the physics of the pulse, the mechanism behind the FRBs emission is still unknown. From FRBs data with known host galaxies, the redshift is directly measured and can be combined with estimates of the $DM$ to constrain the cosmological parameters, such as the baryon number density and the Hubble constant. However, the poor knowledge of the fraction of baryonic mass in the intergalactic medium ($f_{IGM}$) and its degeneracy with the cosmological parameters impose limits on the cosmological application of FRBs. In this work we present a cosmological model-independent method to determine the evolution of $f_{IGM}$ combining the latest FRBs observations with localized host galaxy and current supernovae data. We consider constant and time-dependent $f_{IGM}$ parameterizations and show, through a Bayesian model selection analysis, that a conclusive answer about the time-evolution of $f_{IGM}$ depend strongly on the $DM$ fluctuations due to the spatial variation in cosmic electron density ($\delta$). In particular, our analysis show that the evidence varies from strong (in favor of a growing evolution of $f_{IGM}$ with redshift) to inconclusive, as larger values of $\delta$ are considered.