We report the rest-frame ultraviolet luminosity function of g-dropout galaxies in 177 protocluster candidates (PC UVLF) at z ∼ 4 selected in the Hyper Suprime-Cam Subaru Strategic Program. Comparing it with the UVLF of field galaxies at the same redshift, we find that the PC UVLF shows a significant excess toward the bright end. This excess cannot be explained by the contribution of only active galactic nuclei, and we also find that this excess is more significant in higher density 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 ∼ 4. We also estimate the star formation rate density (SFRD) in protocluster regions as ≃6%-20% of the cosmic SFRD, based on the measured PC UVLF after correction for the selection incompleteness in our protocluster sample. This high value suggests that protoclusters make a nonnegligible contribution to the cosmic SFRD at z ∼ 4, as previously suggested by simulations. Our results suggest that protoclusters are essential components for galaxy evolution at z ∼ 4.

We have obtained three-dimensional maps of the universe in ∼200 × 200 × 80 comoving Mpc3 (cMpc3) volumes each at z = 5.7 and 6.6 based on a spectroscopic sample of 179 galaxies that achieves ⪆80% completeness down to the Lyα luminosity of, based on our Keck and Gemini observations and the literature. The maps reveal filamentary large-scale structures and two remarkable overdensities made out of at least 44 and 12 galaxies at z = 5.692 (z57OD) and z = 6.585 (z66OD), respectively, making z66OD the most distant overdensity spectroscopically confirmed to date, with >10 spectroscopically confirmed galaxies. We compare spatial distributions of submillimeter galaxies at z ≃ 4-6 with our z = 5.7 galaxies forming the large-scale structures, and detect a 99.97% signal of cross-correlation, indicative of a clear coincidence of dusty star-forming galaxy and dust-unobscured galaxy formation at this early epoch. The galaxies in z57OD and z66OD are actively forming stars with star-formation rates (SFRs) ⪆5 times higher than the main sequence, and particularly the SFR density in z57OD is 10 times higher than the cosmic average at the redshift (a.k.a. the Madau-Lilly plot). Comparisons with numerical simulations suggest that z57OD and z66OD are protoclusters that are progenitors of the present-day clusters with halo masses of ∼1014 M o˙