An Analysis of ALMA Deep Fields and the Perceived Dearth of High-z
  Galaxies
  Deep, pencil-beam surveys from ALMA at 1.1-1.3mm have uncovered an apparent
absence of high-redshift dusty galaxies, with existing redshift distributions
peaking around $z\sim1.5-2.5$. This has led to a perceived dearth of dusty
systems at $z>4$, and the conclusion, according to some models, that the early
Universe was relatively dust-poor. In this paper, we extend the backward
evolution galaxy model described by Casey et al. (2018) to the ALMA regime (in
depth and area) and determine that the measured number counts and redshift
distributions from ALMA deep field surveys are fully consistent with
constraints of the infrared luminosity function (IRLF) at $z<2.5$ determined by
single-dish submillimeter and millimeter surveys conducted on much larger
angular scales ($\sim1-10$deg$^{2}$). We find that measured 1.1-1.3mm number
counts are most constraining for the measurement of the faint-end slope of the
IRLF at $z<2.5$ instead of the prevalence of dusty galaxies at $z>4$. Recent
studies have suggested that UV-selected galaxies at $z>4$ may be particularly
dust-poor, but we find their millimeter-wave emission cannot rule out
consistency with the Calzetti dust attenuation law even by assuming relatively
typical, cold-dust ($T_{\rm dust}\approx30\,$K) SEDs. Our models suggest that
the design of ALMA deep fields requires substantial revision to constrain the
prevalence of $z>4$ early Universe obscured starbursts. The most promising
avenue for detection and characterization of such early dusty galaxies will
come from future ALMA 2mm blank field surveys covering a few hundred
arcmin$^{2}$ and the combination of existing and future dual-purpose 3mm
datasets.
