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Fast radio bursts (FRBs) are millisecond transients of unknown origin(s)occurring at cosmological distances. Here we, for the first time, showtime-integrated-luminosity functions and volumetric occurrence rates ofnon-repeating and repeating FRBs against redshift. Thetime-integrated-luminosity functions of non-repeating FRBs do not show anysignificant redshift evolution. The volumetric occurrence rates are almostconstant during the past $\sim$10 Gyr. The nearly-constant rate is consistentwith a flat trend of cosmic stellar-mass density traced by old stellarpopulations. Our findings indicate that the occurrence rate of non-repeatingFRBs follows the stellar-mass evolution of long-living objects with $\sim$Gyrtime scales, favouring e.g. white dwarfs, neutron stars, and black holes, aslikely progenitors of non-repeating FRBs. In contrast, the occurrence rates ofrepeating FRBs may increase towards higher redshifts in a similar way to thecosmic star formation-rate density or black hole accretion-rate density if theslope of their luminosity function does not evolve with redshift. Short-livingobjects with $\lesssim$ Myr time scales associated with young stellarpopulations (or their remnants, e.g., supernova remnants, young pulsars, andmagnetars) or active galactic nuclei might be favoured as progenitor candidatesof repeating FRBs.

No redshift evolution of non-repeating fast radio-burst rates