Investigating Cosmological Models and the Hubble Tension using Localized Fast Radio Bursts

We use the dispersion measure (DM) and redshift measurements of 24 localized fast radio bursts (FRBs) to compare cosmological models and investigate the Hubble tension. Setting a flat prior on the DM contribution from the Milky Way's halo, $\mathrm{DM_{halo}^{MW}}\in[5,\;80]\;\mathrm{pc\;cm^{-3}}$, the best fit for flat $\Lambda$CDM is obtained with a Hubble constant $H_0=95.8^{+7.8}_{-9.2}\;\mathrm{km\;s^{-1}\;Mpc^{-1}}$ and a median matter density $\Omega_{\mathrm{m}}\approx0.66$. The best fit for the $R_{\mathrm{h}}=ct$ universe is realized with $H_0=94.2^{+5.6}_{-6.2}\;\mathrm{km\;s^{-1}\;Mpc^{-1}}$. We emphasize that the $H_0$ measurement depends sensitively on the $\mathrm{DM_{halo}^{MW}}$ prior. Since flat $\Lambda$CDM has one more free parameter, $R_{\mathrm{h}}=ct$ is favored by the Bayesian Information Criterion (BIC) with a likelihood of $\sim73\%$ versus $\sim27\%$. Through simulations, we find that if the real cosmology is $\Lambda$CDM, a sample of $\sim1,150$ FRBs in the redshift range $0<z<3$ would be sufficient to rule out $R_{\mathrm{h}}=ct$ at a $3\sigma$ confidence level, while $\sim550$ FRBs would be necessary to rule out $\Lambda$CDM if the real cosmology is instead $R_{\mathrm{h}}=ct$. The required sample sizes are different, reflecting the fact that the BIC imposes a severe penalty on the model with more free parameters. We further adopt a straightforward method of deriving an upper limit to $H_{0}$, without needing to consider the poorly known probability distribution of the DM contributed by the host galaxy. The theoretical DM contribution from the intergalactic medium ($\mathrm{DM_{IGM}}$) at any $z$ is proportional to $H_0$. Thus, requiring the extragalactic $\mathrm{DM_{ext}}$ to be larger than $\mathrm{DM_{IGM}}$ delimits $H_0$ to the upside. Assuming flat $\Lambda$CDM, we have $H_0<89.0\;\mathrm{km\;s^{-1}\;Mpc^{-1}}$ at a 95\% confidence level.