# Cosmology-independent estimate of the fraction of baryon mass in the IGM from fast radio burst observations

## TL;DR

This paper introduces a cosmology-independent method to estimate the fraction of baryons in the intergalactic medium using fast radio burst observations with known luminosity distances, achieving about 12% accuracy with 50 measurements.

## Contribution

The paper proposes a novel approach to determine the baryon fraction in the IGM independently of cosmological models using FRB data with luminosity distances.

## Key findings

- Unbiased estimate of $f_{IGM}$ with ~12% uncertainty from 50 measurements.
- Method allows measurement of local host galaxy DM contribution.
- Estimates $f_{IGM}$ as a function of redshift, assuming mild evolution.

## Abstract

The excessive dispersion measure (DM) of fast radio bursts (FRBs) has been proposed to be a powerful tool to study intergalactic medium (IGM) and to perform cosmography. One issue is that the fraction of baryons in the IGM, $f_{\rm IGM}$, is not properly constrained. Here we propose a method of estimating $f_{\rm IGM}$ using a putative sample of FRBs with the measurements of both DM and luminosity distance $d_{\rm L}$. The latter can be obtained if the FRB is associated with a distance indicator (e.g. a gamma-ray burst or a gravitational wave event), or the redshift $z$ of the FRB is measured and $d_{\rm L}$ at the corresponding $z$ is available from other distance indicators (e.g. type Ia supernovae) at the same redshift. Since $d_{\rm L}/{\rm DM}$ essentially does not depend on cosmological parameters, our method can determine $f_{\rm IGM}$ independent of cosmological parameters. We parameterize $f_{\rm IGM}$ as a function of redshift and model the DM contribution from a host galaxy as a function of star formation rate. Assuming $f_{\rm IGM}$ has a mild evolution with redshift with a functional form and by means of Monte Carlo simulations, we show that an unbiased and cosmology-independent estimate of the present value of $f_{\rm IGM}$ with a $\sim 12\%$ uncertainty can be obtained with 50 joint measurements of $d_{\rm L}$ and DM. In addition, such a method can also lead to a measurement of the mean value of DM contributed from the local host galaxy.