The VIMOS Ultra Deep Survey: The reversal of the star-formation rate $-$
  density relation at $2 < z < 5$
  Utilizing spectroscopic observations taken for the VIMOS Ultra-Deep Survey
(VUDS), new observations from Keck/DEIMOS, and publicly available observations
of large samples of star-forming galaxies, we report here on the relationship
between the star formation rate (SFR) and the local environment
($\delta_{gal}$) of galaxies in the early universe ($2<z<5$). Unlike what is
observed at lower redshifts ($z<2$), we observe a definite, nearly monotonic
increase in the average SFR with increasing galaxy overdensity over more than
an order of magnitude in $\delta_{gal}$. The robustness of this trend is
quantified by accounting for both uncertainties in our measurements and galaxy
populations that are either underrepresented or not present in our sample and
find that the trend remains significant under all circumstances. This trend
appears to be primarily driven by the fractional increase of galaxies in high
density environments that are more massive in their stellar content and are
forming stars at a higher rate than their less massive counterparts. We find
that, even after stellar mass effects are accounted for, there remains a weak
but significant SFR-$\delta_{gal}$ trend in our sample implying that additional
environmentally-related processes are helping to drive this trend. We also find
clear evidence that the average SFR of galaxies in the densest environments
increases with increasing redshift. These results lend themselves to a picture
in which massive gas-rich galaxies coalesce into proto-cluster environments at
$z\sim3$, interact with other galaxies or with a forming large-scale medium,
subsequently using or losing most of their gas in the process, and begin to
seed the nascent red sequence that is present in clusters at slightly lower
redshifts.
