X. D. Jia NJU, D. H. Gao NJU, J. H. Chen NJU, Q. Wu NJU, S. X. Yi NJU, F. Y. Wang NJU

Fast radio bursts (FRBs) are enigmatic millisecond-duration radio transients whose physical origins remain debated. To shed light on this, we analyze the CHIME/FRB Catalog 2. By using the probability distribution of dispersion measured (DM) derived from the IllustrisTGN simulation, we compute the pseudo-redshift with $1σ$ error for each FRB. To derive the FRB luminosity function and event rate, we employ a non-parametric statistical method. Building upon Efron-Petrosian method, we find strong luminosity evolution with redshift, well described by $L_0 \propto (1+z)^{6.38}$. After de-evolving this trend, we apply Lynden-Bell's $C^-$ method to derive the comoving FRB formation rate which is found to decline rapidly at high redshift, following $ρ(z) \propto (1+z)^{-5.38 \pm 0.02}$. We also test the robustness of our results by considering the upper and lower limits of pseudo-redshifts, and different flux limits of CHIME. Similar results are found. This steep decline is inconsistent with a direct tracing of the cosmic star formation rate, but closely resembles the redshift evolution of short gamma-ray bursts-systems linked to compact object mergers. Our results support that the origin of FRBs is associated with old populations, such as neutron stars and black holes.