Possible bias of the constraints on the Hubble constant owing to the quasi-Gaussian distribution of DM_IGM in fast radio bursts^*

Fast radio bursts (FRBs) are useful cosmological probes with numerous applications in cosmology. The distribution of the dispersion measurement contribution from the intergalactic medium is a key issue. A quasi-Gaussian distribution has been used to replace the traditional Gaussian distribution, yielding promising results. However, this study suggests that there may be additional challenges in its application. We used 35 well-localized FRBs to constrain the Hubble constant $H_0$ along with two FRB-related parameters, yielding $H_0=60.99^{+4.57}_{-4.90}\ {\rm{km\; s^{-1}}\; Mpc^{-1}}$. The best-fitting Hubble constant $H_0$ is smaller than the value obtained from the Cosmic Microwave Background (CMB), which may be caused by the small sample size of current FRB data. Monte Carlo simulations indicate that a set of 100 simulated FRBs provides a more precise fitting result for the Hubble constant. However, the precision of the Hubble constant does not improve when further enlarging the FRB sample. Additional simulations reveal a systematic deviation in the fitting results of $H_0$, attributed to the quasi-Gaussian distribution of the dispersion measure in the intergalactic medium. Despite this, the results remain reliable within 1σ uncertainty, assuming that a sufficient number of FRB data points are available.