  The intensity of the diffuse ~ 1 - 4 micron sky emission from which solar
system and Galactic foregrounds have been subtracted is in excess of that
expected from energy released by galaxies and stars that formed during the z <
5 redshift interval (Arendt & Dwek 2003, Matsumoto et al. 2005). The spectral
signature of this excess near-infrared background light (NIRBL) component is
almost identical to that of reflected sunlight from the interplanetary dust
cloud, and could therefore be the result of the incomplete subtraction of this
foreground emission component from the diffuse sky maps. Alternatively, this
emission component could be extragalactic. Its spectral signature is consistent
with that of redshifted continuum and recombination line emission from HII
regions formed by the first generation of very massive stars. In this paper we
analyze the implications of this spectral component for the formation rate of
these Population III stars, the redshift interval during which they formed, the
reionization of the universe and evolution of collapsed halo masses. We find
that to reproduce the intensity and spectral shape of the NIRBL requires a peak
star formation rate that is higher by about a factor of 4 to 10 compared to
those derived from hierarchical models. Furthermore, an extragalactic origin
for the NIRBL leads to physically unrealistic absorption-corrected spectra of
distant TeV blazars. All these results suggest that Pop III stars contribute
only a fraction of the NIRBL intensity with zodiacal light, star forming
galaxies, and/or non-nuclear sources giving rise to the remaining fraction.
