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.
Categories: astro-ph.CO astro-ph.HE