GOLDRUSH. IV. Luminosity Functions and Clustering Revealed with 4,000,000 Galaxies at z 2-7: Galaxy-AGN Transition, Star Formation Efficiency, and Implication for Evolution at z > 10

We present new measurements of rest-UV luminosity functions and angular correlation functions from 4,100,221 galaxies at z ~ 2-7 identified in the Subaru/Hyper Suprime-Cam survey and CFHT Large Area U-band Survey. The obtained luminosity functions at z ~ 4-7 cover a very wide UV luminosity range of ~ $0.002\mbox{--}2000{L}_{\mathrm{UV}}^{* }$ combined with previous studies, confirming that the dropout luminosity function is a superposition of the active galactic nucleus (AGN) luminosity function dominant at M _UV ≲ -24 mag and the galaxy luminosity function dominant at M _UV ≳ -22 mag, consistent with galaxy fractions based on 1037 spectroscopically identified sources. Galaxy luminosity functions estimated from the spectroscopic galaxy fractions show the bright-end excess beyond the Schechter function at ≳2σ levels, possibly made by inefficient mass quenching, low dust obscuration, and/or hidden AGN activity. By analyzing the correlation functions at z ~ 2-6 with HOD models, we find a weak redshift evolution (within 0.3 dex) of the ratio of the star formation rate (SFR) to the dark matter accretion rate, $\mathrm{SFR}/{\dot{M}}_{{\rm{h}}}$ , indicating the almost constant star formation efficiency at z ~ 2-6, as suggested by our earlier work at z ~ 4-7. Meanwhile, the ratio gradually increases with decreasing redshift at z < 5 within 0.3 dex, which quantitatively reproduces the cosmic SFR density evolution, suggesting that the redshift evolution is primarily driven by the increase of the halo number density due to the structure formation, and the decrease of the accretion rate due to the cosmic expansion. Extrapolating this calculation to higher redshifts assuming the constant efficiency suggests a rapid decrease of the SFR density at z > 10 with ∝ 10^-0.5(1+z), which will be directly tested with the James Webb Space Telescope.