  The emergence of passive galaxies in the early Universe results from the
interplay among the processes responsible for their rapid assembly and for the
abrupt shut-down of their SF. Investigating the individual properties and
demographics of early passive galaxies will improve our understanding of these
mechanisms. In this work we present a follow-up analysis of the z>3 passive
galaxy candidates selected by Merlin et al. (2019) in the CANDELS fields. We
begin by first confirming the accuracy of their passive classification by
exploiting their sub-mm emission to demonstrate the lack of ongoing SF. Using
archival ALMA observations we are able to confirm at least 61% of the observed
candidates as passive. While the remainder lack sufficiently deep data for
confirmation, we are able to validate the entire sample in a statistical sense.
We then estimate the Stellar Mass Function (SMF) of all 101 passive candidates
in three redshift bins from z=5 to z=3. We adopt a stepwise approach that has
the advantage of taking into account photometric errors, observational
incompleteness, and the Eddington bias without any a-posteriori correction. We
observe a pronounced evolution in the SMF around z~4, indicating that we are
witnessing the emergence of the passive population at this epoch. Massive
(M>10^11Msun) passive galaxies, only accounting for a small (<10%) fraction of
galaxies at z>4, become dominant at later epochs. Thanks to a combination of
photometric quality, sample selection and methodology, we overall find a higher
density of passive galaxies than previous works. The comparison with
theoretical predictions, despite a qualitative agreement, denotes a still
incomplete understanding of the physical processes responsible for the
formation of these galaxies. Finally, we extrapolate our results to predict the
number of early passive galaxies expected in surveys carried out with future
facilities.
