The LGRBs Redshift and Jet Opening Angle Distributions and the Hubble Constant $H_0$

Using the Swift-Perley sample, Le, Ratke, & Mehta performed a study of the rate density of LGRBs with an assumed broken power-law GRB spectrum. They obtained a GRB-burst-rate functional form that fits the preSwift~and Swift~redshift cumulative distributions at all redshifts with an assumed Hubble constant of $H_0 = 72 \, {\rm km \, s^{-1} \, Mpc^{-1}}$. Further analysis indicated that the cumulative redshift distribution is weakly sensitive to variations in the Hubble constant $H_0$, whereas the corresponding differential burst-rate distribution exhibits greater sensitivity. In this paper, we extend this analysis by comparing model predictions for different values of $H_0$ with the observed cumulative and differential redshift and jet-opening angle distributions, while adopting the same GRB framework and observational samples. We find that both the cumulative and differential distributions depend only weakly on variations in $H_0$, and the model predictions using $H_0 \approx 68 - 80 \, {\rm km \, s^{-1} \, Mpc^{-1}}$ provide agreement with the observed LGRB distributions.