Constraining the baryon fraction in the extragalactic diffuse ionized gas with 124 localized fast radio bursts

Fast radio bursts (FRBs) are increasingly recognized as powerful cosmological tools for constraining the baryon fraction in extragalactic diffuse ionized gas, presenting a promising approach to address the missing baryon problem. In this paper, we constrain the baryon fraction in extragalactic diffuse ionized gas ($f_\mathrm{d}$) utilizing the latest sample of 124 localized FRBs across three different cosmological models. Our analysis models the probability distribution of the extragalactic diffuse ionized gas dispersion measure with a form that accurately reproduces mock observations. For a constant $f_\mathrm{d}$ model, we find that more than 90\% of baryons reside in the diffuse ionized gas phase. This result is robust against the choice of dark-energy parametrization under the current combination of datasets, although the fitted cosmological parameters shift accordingly. We also find that the inferred $f_\mathrm{d}$ is sensitive to the assumed dispersion measure distributions of both the Milky Way halo and the FRB host galaxies. Furthermore, the current data do not show statistically significant evidence for redshift evolution in $f_\mathrm{d}$, but the constraints are limited by the redshift distribution of the sample. Our conclusions are insensitive to the adopted baryonic feedback parameters and to the dispersion measure selection effect. These results provide strong evidence that the majority of the missing baryons reside in the diffuse ionized intergalactic medium.