Estimating the baryon fraction in the IGM from well-localized FRBs and DESI data

Current measurements of Baryon Acoustic Oscillations (BAO) from the Dark Energy Spectroscopic Survey (DESI DR2), when combined with data from Type Ia supernovae (SNe), challenge the observational viability of the $\Lambda$-Cold Dark Matter ($\Lambda$CDM) model, motivating combinations of independent datasets to estimate cosmological quantities. In a previous communication, we presented a cosmological independent method to constrain the baryon fraction in the IGM ($f_{\mathrm{IGM}}$), where we derived relevant expressions for the dispersion measure ($\mathrm{DM}$) in terms of luminosity distance, allowing us to estimate $f_{\mathrm{IGM}}$ combining directly measurements of 17 well-localized FRBs and 1048 SNe from the Pantheon catalog. Here we revisit this method to constrain $f_{\mathrm{IGM}}$, considering two parameterizations for the $f_{\mathrm{IGM}}$: constant and time-dependent. We expand our sample by combining 107 well-localized Fast Radio Bursts (FRBs) with BAO measurements from DESI DR2 and SNe observations from DESY5, and the Pantheon+ catalog. We find through a Bayesian model selection analysis that a conclusive answer about the evolution of $f_{\mathrm{IGM}}$ cannot be achieved from the current FRBs observational data. In particular, our results show weak evidence in favor of the constant case.