Generalized Distributions of Host Dispersion Measures in the Fast Radio Burst Cosmology
Authors
Jing-Yi Jia
Da-Chun Qiang
Lin-Yu Li
Hao Wei
Abstract
As is well known, Hubble tension is one of the most serious challenges in cosmology to date. So, it is of interest to measure the Hubble constant by using some new probes independent of cosmic microwave background (CMB) and type Ia supernovae (SNIa). One of the promising probes is the fast radio bursts (FRBs), which could be useful in cosmology. In the literature, the methodology proposed by Macquart {\it et al.} has been widely used, in which both $\rm DM_{IGM}$ and $\rm DM_{host}$ are described by probability distribution functions. Recently, it was found that in order to obtain a Hubble constant $H_0$ consistent with the ones of Planck 2018 and SH0ES by using the current ${\cal O}(100)$ localized FRBs, an unusually large $f_{\rm IGM}$ fairly close to its upper bound $1$ is required, if the narrow prior bounded by $0.5$ for the parameter $F$ in the distribution of $\rm DM_{IGM}$ was used. In fact, a small $F$ is the key to make $H_0$ larger. In the present work, we consider a loose prior for the parameter $F$, and find an unusually low $H_0$ by using 125 localized FRBs. We show that the model with loose $F$ prior is strongly preferred over the one with narrow $F$ prior in all terms of the Bayesian evidence and the information criteria AIC, BIC. So, the great Hubble tension between FRBs, Planck 2018 and SH0ES should be taken seriously. Instead of modifying $σ_Δ=Fz^{-0.5}$ in the distribution of $\rm DM_{IGM}$, here we try to find a new way out by generalizing the distribution of $\rm DM_{host}$ with varying location and scale parameters $\ell$ and $e^μ$, respectively. We find that $H_0$ can be consistent with the ones of Planck 2018 and SH0ES in all cases. All the Bayesian evidence and the information criteria AIC, BIC for the generalized distributions of $\rm DM_{host}$ are overwhelmingly strong.
