Evidence for a Delayed Progenitor Population for CHIME Nonrepeating Fast Radio Bursts from a Self-consistent Forward and Backward Inference Framework

Fast radio bursts (FRBs) are luminous extragalactic radio transients whose physical origins remain uncertain. Using over 1000 nonrepeating events from CHIME/FRB Catalog 2, we infer the intrinsic FRB demographics with a self-consistent framework that combines backward nonparametric inference and forward population synthesis while accounting for a probabilistic dispersion measure–redshift relation, baseband-to-catalog fluence corrections, and an injection-calibrated multidimensional selection function. We first apply a backward nonparametric method, the weighted Lynden-Bell C − estimator, to recover the intrinsic redshift and energy distributions without assuming any population model. Independently, we perform forward Monte Carlo population synthesis in observable dispersion measure–fluence space, treating candidate intrinsic redshift and energy distributions as population hypotheses and comparing the resulting selected synthetic catalogs with observations. We find that the intrinsic redshift distribution peaks at z ∼ 1, below the cosmic star formation history (SFH) peak at z ∼ 1.7, indicating strong tension with a pure SFH-tracking scenario, suggesting that at least some FRBs are delayed with respect to SFH. The intrinsic energy distribution is consistent with a power law with index α ≈ 1.9 and steepens at higher energies. We find no significant evidence for an intrinsic redshift–energy correlation.