  We present an analysis of all prime HST legacy fields spanning >800 arcmin^2
for the search of z~10 galaxy candidates and the study of their UV luminosity
function (LF). In particular, we present new z~10 candidates selected from the
full Hubble Frontier Field (HFF) dataset. Despite the addition of these new
fields, we find a low abundance of z~10 candidates with only 9 reliable sources
identified in all prime HST datasets that include the HUDF09/12, the HUDF/XDF,
all the CANDELS fields, and now the HFF survey. Based on this comprehensive
search, we find that the UV luminosity function decreases by one order of
magnitude from z~8 to z~10 at all luminosities over a four magnitude range.
This also implies a decrease of the cosmic star-formation rate density by an
order of magnitude within 170 Myr from z~8 to z~10. We show that this
accelerated evolution compared to lower redshift can entirely be explained by
the fast build-up of the dark matter halo mass function at z>8. Consequently,
the predicted UV LFs from several models of galaxy formation are in good
agreement with this observed trend, even though the measured UV LF lies at the
low end of model predictions. In particular, the number of only 9 observed
candidate galaxies is lower, by ~50%, than predicted by galaxy evolution
models. The difference is generally still consistent within the Poisson and
cosmic variance uncertainties. However, essentially all models predict larger
numbers than observed. We discuss the implications of these results in light of
the upcoming James Webb Space Telescope mission, which is poised to find much
larger samples of z~10 galaxies as well as their progenitors at less than 400
Myr after the Big Bang.
