  We present a new measurement of the evolving galaxy far-IR luminosity
function (LF) extending out to redshifts z~5, with resulting implications for
the level of dust-obscured star-formation density in the young Universe. To
achieve this we have exploited recent advances in sub-mm/mm imaging with
SCUBA-2 on the James Clerk Maxwell Telescope (JCMT) and the Atacama Large
Millimeter/Submillimeter Array (ALMA), which together provide unconfused
imaging with sufficient dynamic range to provide meaningful coverage of the
luminosity-redshift plane out to z>4. Our results support previous indications
that the faint-end slope of the far-IR LF is sufficiently flat that comoving
luminosity-density is dominated by bright objects (~L*). However, we find that
the number-density/luminosity of such sources at high redshifts has been
severely over-estimated by studies that have attempted to push the
highly-confused Herschel SPIRE surveys beyond z~2. Consequently we confirm
recent reports that cosmic star-formation density is dominated by UV-visible
star formation at z>4. Using both direct (1/Vmax) and maximum likelihood
determinations of the LF, we find that its high-redshift evolution is well
characterized by continued positive luminosity evolution coupled with negative
density evolution (with increasing redshift). This explains why bright sub-mm
sources continue to be found at z>5, even though their integrated contribution
to cosmic star-formation density at such early times is very small. The
evolution of the far-IR galaxy LF thus appears similar in form to that already
established for active galactic nuclei, possibly reflecting a similar
dependence on the growth of galaxy mass.
