Constraints on the baryon density from fast radio bursts using a non-parametric reconstruction of the Hubble parameter

In this study, we use a sample of 130 well-localized fast radio bursts (FRBs) to constrain the physical baryon density $\Omega_{\rm b}h^2$, and the astrophysical contribution from host galaxies. The cosmological dependence entering the intergalactic dispersion measure is described through a non-parametric reconstruction of the Hubble parameter $H(z)$ obtained from cosmic chronometer data using the \texttt{ReFANN} neural-network framework, independently of the FRB sample. Within a Bayesian analysis, we jointly infer $\Omega_{\rm b}h^2$ and the parameters of a log-normal host-galaxy distribution, namely its median $e^\mu$ and logarithmic scatter $\sigma_{\rm host}$, using both real FRB data and a mock catalog. For the real sample, we obtain $\Omega_{\rm b}h^2=0.02236\pm0.00090$, $e^\mu=178.15^{+16.51}_{-16.97}~\mathrm{pc}\,\mathrm{cm}^{-3}$, and $\sigma_{\rm host}=0.794^{+0.064}_{-0.067}$. For the mock catalog, we find $\Omega_{\rm b}h^2=0.02248\pm0.00018$, $e^\mu=182.36^{+6.83}_{-6.48}~\mathrm{pc}\,\mathrm{cm}^{-3}$, and $\sigma_{\rm host}=0.711^{+0.024}_{-0.025}$. The baryon density constraint from the real FRB sample is in excellent agreement with both Big Bang Nucleosynthesis and Planck CMB determinations, differing from their central values by only $\simeq 0.05\%$. The mock analysis further illustrates the potential of future FRB samples, reducing the uncertainty on $\Omega_{\rm b}h^2$ to the sub-percent level while remaining statistically consistent with early-Universe constraints. Our findings show that combining FRB dispersion measures with a non-parametric reconstruction of the expansion history provides a robust pathway to constrain both cosmological and astrophysical parameters, establishing FRBs as a complementary low-redshift probe of the baryon density.