Evidence for a Delayed Progenitor Population for CHIME non-repeating Fast Radio Bursts using a Self-Consistent Forward and Backward Inference Framework

Fast radio bursts (FRBs) are luminous extragalactic radio transients whose physical origins remain uncertain. Using over one thousand non-repeating events from CHIME/FRB Catalog 2, we infer the intrinsic FRB demographics with a self-consistent framework that combines backward non-parametric inference and forward population synthesis while accounting for probabilistic dispersion measure–redshift estimates, baseband-to-catalog fluence corrections, and the latest fuzzy multidimensional selection function. We first apply a backward non-parametric 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 $z\sim 1$, significantly lower than the cosmic star formation history (SFH) peak at $z\sim 1.7$, indicating clear 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 of index $\alpha \approx 1.9$ and steepens at higher energies. We find no significant evidence for a redshift-energy distribution correlation.