  Fast radio bursts (FRBs) are mysterious millisecond pulses in radio, most of
which originate from distant galaxies. Revealing the origin of FRBs is becoming
central in astronomy. The redshift evolution of the FRB energy function, i.e.,
the number density of FRB sources as a function of energy, provides important
implications for the FRB progenitors. Here we show the energy functions of FRBs
selected from the recently released Canadian Hydrogen Intensity Mapping
Experiment (CHIME) catalogue using the $V_{\rm max}$ method. The $V_{\rm max}$
method allows us to measure the redshift evolution of the energy functions as
it is without any prior assumption on the evolution. We use a homogeneous
sample of 164 non-repeating FRB sources, which are about one order of magnitude
larger than previously investigated samples. The energy functions of
non-repeating FRBs show Schechter function-like shapes at $z\lesssim1$. The
energy functions and volumetric rates of non-repeating FRBs decrease towards
higher redshifts similar to the cosmic stellar-mass density evolution: there is
no significant difference between the non-repeating FRB rate and cosmic
stellar-mass density evolution with a 1\% significance threshold, whereas the
cosmic star-formation rate scenario is rejected with a more than 99\%
confidence level. Our results indicate that the event rate of non-repeating
FRBs is likely controlled by old populations rather than young populations
which are traced by the cosmic star-formation rate density. This suggests old
populations such as old neutron stars and black holes as more likely
progenitors of non-repeating FRBs.
