The quasi-Gaussian distribution of DMIGM in fast radio bursts may bias the constraints on the Hubble constant

Fast radio bursts (FRBs) are useful cosmological probes with numerous applications in cosmology. The distribution of the dispersion measure contribution from the intergalactic medium is a key issue. A quasi-Gaussian distribution has been used to replace the traditional Gaussian distribution, which yields promising results. However, our work suggests that there may be additional challenges in its application. Here we use 35 well-localized FRBs to constrain the Hubble constant H0 along with two FRB-related parameters, yielding H0 =60.99+4.57 −4.90 km s-1 Mpc-1. The best-fitting Hubble constant H0 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. But the precision of the Hubble constant does not improve when further enlarging the FRB sample. Further simulations reveal a systematic deviation in the fitting results of H0, attributed to the quasi-Gaussian distribution of dispersion measure in the intergalactic medium. Despite this, the results remain reliable within the 1σ uncertainty, assuming a sufficient number of FRB data are available.