Revealing the formation histories of the first stars with the cosmic
  near-infrared background
  The cosmic near-infrared background (NIRB) offers a powerful integral probe
of radiative processes at different cosmic epochs, including the
pre-reionization era when metal-free, Population III (Pop III) stars first
formed. While the radiation from metal-enriched, Population II (Pop II) stars
likely dominates the contribution to the observed NIRB from the reionization
era, Pop III stars -- if formed efficiently -- might leave characteristic
imprints on the NIRB thanks to their strong Ly$\alpha$ emission. Using a
physically-motivated model of first star formation, we provide an analysis of
the NIRB mean spectrum and anisotropy contributed by stellar populations at
$z>5$. We find that in circumstances where massive Pop III stars persistently
form in molecular cooling haloes at a rate of a few times $10^{-3}\,M_\odot \
\mathrm{yr}^{-1}$, before being suppressed towards the epoch of reionization
(EoR) by the accumulated Lyman-Werner background, a unique spectral signature
shows up redward of $1\,\mu$m in the observed NIRB spectrum sourced by galaxies
at $z>5$. While the detailed shape and amplitude of the spectral signature
depend on various factors including the star formation histories, IMF, LyC
escape fraction and so forth, the most interesting scenarios with efficient Pop
III star formation are within the reach of forthcoming facilities such as the
Spectro-Photometer for the History of the Universe, Epoch of Reionization and
Ices Explorer (SPHEREx). As a result, new constraints on the abundance and
formation history of Pop III stars at high redshifts will be available through
precise measurements of the NIRB in the next few years.
