Fast Radio Bursts as cosmological proxies: estimating the Hubble constant

One of the most challenging problems in cosmology is the Hubble tension, a discrepancy in the predicted expansion rate of the Universe. We leverage the sensitivity of the Dispersion Measure (DM) from Fast Radio Bursts (FRBs) with the Hubble factor to investigate the Hubble tension. We build a catalog of 98 localized FRBs and an independent mock catalog and employ 3 methods to calculate the best value of the $H_0$: i) the mean of $H_0$ values obtained through direct calculation, ii) the maximum likelihood estimate (MLE) and iii) the reconstruction of the cosmic expansion history $H(z)$ using two DM-$z$ relations. When the confirmed FRBs is employed, our predictions are compatible with reports from the Planck+2018, with $H_0=65.13\pm2.52\,\text{km/s/Mpc}$ and $57.67\pm11.99\,\text{km/s/Mpc}$ for MLE and the arithmetic mean, respectively. If we assume a linear and a power-law function for the DM-$z$ relation, our predictions for $H_0$ are $51.27^{+3.80}_{-3.31}\,\text{km/s/Mpc}$ and $77.09^{+8.89}_{-7.64}\,\text{km/s/Mpc}$, respectively. Using 100 mock catalogs of simulated FRBs, we obtain larger values for $H_0$ with all methods considered: $H_{0;\text{ Like}}=67.30\pm0.91\,\text{km/s/Mpc}$, $H_{0;\text{ Mean}}=66.21\pm3.46\,\text{km/s/Mpc}$, $H_{0;\text{ Median}}=66.10\pm1.89\,\text{km/s/Mpc}$, $H_{0;\text{Linear}}=54.34\pm1.57\,\text{km/s/Mpc}$ and $H_{0;\text{Power-law}}=91.84\pm1.82\,\text{km/s/Mpc}$ for the MLE, the arithmetic mean, and linear and power-law $\text{DM}-z$ relations, respectively. Our results for mock FRB catalogs increase the statistical precision, ranging from 1.4\% to 5.2\% for the MLE and arithmetic mean. Our result with the MLE applied to synthetic FRBs is at the same level of precision as reports from SH0ES. The increase in the number of confirmed FRBs will provide us, in combination with other observations, a robust prediction of the value of the Hubble constant.