Recent estimates point to abundances of z > 4 sub-millimeter (sub-mm) galaxies far above model predictions. The matter is still debated. According to some analyses the excess may be substantially lower than initially thought and perhaps accounted for by flux boosting and source blending. However, there is no general agreement on this conclusion. An excess of z > 6 dusty galaxies has also been reported albeit with poor statistics. On the other hand, evidence of a top-heavy initial mass function (IMF) in high-z starburst galaxies has been reported in the past decades. This would translate into a higher sub-mm luminosity of dusty galaxies at fixed star formation rate, i.e., into a higher abundance of bright high-z sub-mm galaxies than expected for a universal Chabrier IMF. Exploiting our physical model for high-z proto-spheroidal galaxies, we find that part of the excess can be understood in terms of an IMF somewhat top-heavier than Chabrier. Such IMF is consistent with that recently proposed to account for the low 13C/18O abundance ratio in four dusty starburst galaxies at z = 2-3. However, extreme top-heavy IMFs are inconsistent with the sub-mm counts at z > 4.
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