We use the stellar-mass-selected catalog from the Spitzer Large Area Survey with Hyper-Suprime-Cam (SPLASH) in the COSMOS field to study the environments of galaxies via galaxy density and clustering analyses up to $z sim 2.5$. The clustering strength of quiescent galaxies exceeds that of star-forming galaxies, implying that quiescent galaxies are preferentially located in more massive halos. When using local density measurement, we find a clear positive quiescent fraction--density relation at $z < 1$, consistent with earlier results. However, the quiescent fraction--density relation reverses its trend at intermediate redshifts ($1 < z < 1.5$) with marginal significance (<1.8$sigma$) and is found to be scale dependent (1.6$sigma$). The lower fraction of quiescent galaxies seen in large-scale dense environments, if confirmed to be true, may be associated with the fact that the star formation can be more easily sustained via cold stream accretion in `large-scale high-density regions, preventing galaxies from permanent quenching. Finally, at $z > 1.5$, the quiescent fraction depends little on the local density, even though clustering shows that quiescent galaxies are in more massive halos. We argue that at high redshift the typical halo size falls below $10^{13}$ $M_{odot}$, where intrinsically the local density measurements are so varied that they do not trace the halo mass. Our results thus suggest that in the high-redshift Universe, halo mass may be the key in quenching the star formation in galaxies, rather than the conventionally measured galaxy density.
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