The UV Luminosity Function of Protocluster Galaxies at $z\sim4$: the
  Bright-end Excess and the Enhanced Star Formation Rate Density
  We report the rest-frame ultraviolet luminosity function of $g$-dropout
galaxies in 177 protocluster candidates (PC UVLF) at $z\sim4$ selected in the
Hyper Suprime-Cam Subaru Strategic Program. Comparing with the UVLF of field
galaxies at the same redshift, we find that the PC UVLF shows a significant
excess towards the bright-end. This excess can not be explained by the
contribution of only active galactic nuclei, and we also find that this is more
significant in higher dense regions. Assuming that all protocluster members are
located on the star formation main sequence, the PC UVLF can be converted into
a stellar mass function. Consequently, our protocluster members are inferred to
have a 2.8 times more massive characteristic stellar mass than that of the
field Lyman break galaxies at the same redshift. This study, for the first
time, clearly shows that the enhancement in star formation or stellar mass in
overdense regions can generally be seen as early as at $z\sim4$. We also
estimate the star formation rate density (SFRD) in protocluster regions as
$\simeq 6-20\%$ of the cosmic SFRD, based on the measured PC UVLF after
correcting for the selection incompleteness in our protocluster sample. This
high value suggests that protoclusters make a non-negligible contribution to
the cosmic SFRD at $z\sim4$, as previously suggested by simulations. Our
results suggest that protoclusters are essential components for the galaxy
evolution at $z\sim4$.
