Forecasting constraints on the baryon mass fraction in the IGM from fast radio bursts and type Ia supernovae

Fast Radio Bursts (FRBs) are millisecond transient radio events with a high energy. By identifying the origin of the \textbf{burst}, it is possible to measure the redshift of the host galaxy, which can be used to constrain cosmological and astrophysical parameters and test aspects of fundamental physics when combined with the dispersion measure ($DM$). However, some factors limit the cosmological application of FRBs: (i) the poor modelling of the fluctuations in the $DM$ due to spatial variation in the cosmic electrons density; (ii) the fact that the fraction of baryon mass in the intergalactic medium ($f_{IGM}$) is degenerated with some cosmological parameters; (iii) the limited knowledge about host galaxy contribution ($DM_{host}$). In this work, we investigate the impact of different redshift distribution models of FRBs to constrain the baryon fraction in the IGM and host galaxy contribution. We use a cosmological model-independent method developed in previous work \cite{Lemos2023} to perform the analysis and combine simulated FRB data from Monte Carlo simulation and supernovae data. We assume four distribution models for the FRBs: gamma-ray bursts (GRB), star formation rate (SFR), uniform and equidistant (ED). Also, we consider samples with $N = 15, 30, 100$ and $500$ points and different values of the fluctuations of electron density in the $DM$, $\delta = 0, 100, 200, 400, 230\sqrt{z}$ pc/cm$^{3}$. Our analysis shows that all the distribution models present consistent results within $2\sigma$ for the free parameters $f_{IGM}$ and $DM_{host,0}$ and highlights the crucial role of $DM$ fluctuations in obtaining more precise measurements.