Deep , pencil-beam surveys from ALMA at 1.1–1.3 mm have uncovered an apparent absence of high-redshift dusty galaxies , with existing redshift distributions peaking around z \sim 1.5 - 2.5 .
This has led to a perceived dearth of dusty systems at z \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 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 ( \sim 1–10 deg ^ { 2 } ) .
We find that measured 1.1–1.3 mm number counts are most constraining for the measurement of the faint-end slope of the IRLF at z \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 2.5 instead of the prevalence of dusty galaxies at z \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 4 .
Recent studies have suggested that UV-selected galaxies at z > 4 may be particularly dust-poor , but we find their millimeter-wave emission can not rule out consistency with the Calzetti dust attenuation law , even by assuming relatively typical , cold-dust ( T _ { dust } \approx 30 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 2 mm blank field surveys covering a few hundred arcmin ^ { 2 } and the combination of existing and future dual-purpose 3 mm datasets .