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Generalized Distributions of Host Dispersion Measures in the Fast Radio Burst Cosmology

Jing-Yi Jia, Da-Chun Qiang, Lin-Yu Li, Hao Wei

TL;DR

This work reassesses FRB-based determinations of the Hubble constant by relaxing the prior on the DM fluctuation parameter $F$ and by generalizing the host-galaxy dispersion measure (DM$_{host}$) distribution. Using 125 localized FRBs, the fiducial Macquart model with a log-normal DM$_{host}$ and a DM$_{IGM}$ PDF yields a low $H_0$ (e.g., $H_0\approx45.7$ km s$^{-1}$ Mpc$^{-1}$ for the fiducial priors), while a narrow-$F$ prior can push $H_0$ toward Planck/SH0ES values but is disfavored by Bayesian evidence. By introducing a location parameter $oldsymbol{ extell}$ (and variants) in $ m DM_{host}$, as well as scale modifications via $e^ extmu$, the authors achieve $H_0$ values that are consistent with Planck 2018 and SH0ES across models, with all generalized $ m DM_{host}$ models being overwhelmingly preferred by Bayesian evidence and information criteria (AIC/BIC). The results indicate that a careful modeling of $ m DM_{host}$ is crucial for FRB cosmology and suggest future work on analytic forms for $ extell$ and $e^ extmu$ and potential redshift evolution of DM$_{host}$.

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.

Generalized Distributions of Host Dispersion Measures in the Fast Radio Burst Cosmology

TL;DR

This work reassesses FRB-based determinations of the Hubble constant by relaxing the prior on the DM fluctuation parameter and by generalizing the host-galaxy dispersion measure (DM) distribution. Using 125 localized FRBs, the fiducial Macquart model with a log-normal DM and a DM PDF yields a low (e.g., km s Mpc for the fiducial priors), while a narrow- prior can push toward Planck/SH0ES values but is disfavored by Bayesian evidence. By introducing a location parameter (and variants) in , as well as scale modifications via , the authors achieve values that are consistent with Planck 2018 and SH0ES across models, with all generalized models being overwhelmingly preferred by Bayesian evidence and information criteria (AIC/BIC). The results indicate that a careful modeling of is crucial for FRB cosmology and suggest future work on analytic forms for and and potential redshift evolution of DM.

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 and are described by probability distribution functions. Recently, it was found that in order to obtain a Hubble constant consistent with the ones of Planck 2018 and SH0ES by using the current localized FRBs, an unusually large fairly close to its upper bound is required, if the narrow prior bounded by for the parameter in the distribution of was used. In fact, a small is the key to make larger. In the present work, we consider a loose prior for the parameter , and find an unusually low by using 125 localized FRBs. We show that the model with loose prior is strongly preferred over the one with narrow 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 in the distribution of , here we try to find a new way out by generalizing the distribution of with varying location and scale parameters and , respectively. We find that 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 are overwhelmingly strong.

Paper Structure

This paper contains 9 sections, 63 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The fiducial methodology
  3. The methodology and the data
  4. The Bayesian evidence and the information criteria
  5. The Bayesian evidence and the information criteria
  6. The fiducial model
  7. Generalized distributions of $\bf DM_{host}$ with varying location $\boldsymbol{\ell}$
  8. Generalized distributions of $\bf DM_{host}$ with varying scale $\boldsymbol{e^\mu}$
  9. Concluding remarks

Figures (12)

  • Figure 1: The $1\sigma$ and $2\sigma$ contours for all the free parameters of the fiducial model. The top-right panel is the marginalized probability distribution of the Hubble constant $H_0$ derived from $\Theta$ in Eq. (\ref{['eq4']}) by using $f_{\rm IGM}=0.83$ and $\Omega_b h^2=0.02237$. The mean and $1\sigma$, $2\sigma$ intervals of $H_0$ are given numerically and also shown by the shaded regions. $\Theta$ and $H_0$ are in units of $\rm km/s/Mpc$. $e^\mu$ is in units of ${\rm pc\space cm^{-3}}$. $H_0$ of the Planck 2018 and SH0ES results are also indicated by the vertical dashed lines. See Sec. \ref{['sec2']} for details.
  • Figure 2: The same as in Fig. \ref{['fig1']}, but for the narrow priors used by Macquart et al.Macquart:2020lln. See Sec. \ref{['sec2']} for details.
  • Figure 3: The same as in Fig. \ref{['fig1']}, but for the Loc2s0 model. See Sec. \ref{['sec3']} for details.
  • Figure 4: The same as in Fig. \ref{['fig1']}, but for the Loc3s0 model. See Sec. \ref{['sec3']} for details.
  • Figure 5: The same as in Fig. \ref{['fig1']}, but for the Loc2s model. See Sec. \ref{['sec3']} for details.
  • ...and 7 more figures