A Comprehensive Study of the Energy and Redshift Distributions of the Fast Radio Burst Population Based on the First CHIME/FRB Catalog

Abstract: Fast radio bursts (FRBs) are brief, high-energy bursts of radio waves from extragalactic sources, and their origin remains an open question. In this paper, we perform a comprehensive analysis of the FRB population using the first CHIME/FRB catalog, focusing on their energy and redshift distribution, with careful consideration of selection effects. We investigate a range of models, including the Schechter function and the broken power-law function for the energy distribution, and several redshift evolution models, such as the star formation history (SFH) model, as well as models incorporating time delays relative to the SFH or additional redshift evolution factors. Our results indicate that the energy distribution of FRBs is best described by the Schechter function, with a power-law index of $\gamma = -1.49^{{+0.37}_{-0.27}$} and a characteristic cutoff energy of $E_\mathrm{c} = 2.82^{{+2.43}_{-1.47}} \times 10^{41}$ erg. Furthermore, we find no evidence for redshift evolution in the energy distribution of FRBs. In terms of their redshift distribution, our analysis shows that it follows the cosmic SFH, without requiring additional delayed components or redshift evolution factors, suggesting that most FRBs likely originate from young stellar populations. Simultaneously, we infer a local volumetric rate of $\Phi_0 = 4.68^{{+4.66}_{-2.39}} \times 10^{4} \rm \ Gpc^{-3}yr{-1}$ for $E>10^{39}$ erg. These results, robust against CHIME observational biases, may provide new insights into the underlying properties of the FRB population.