  We use ZFIRE and ZFOURGE observations with the Spectral Energy Distribution
(SED) fitting tool Prospector to reconstruct the star formation histories
(SFHs) of proto-cluster and field galaxies at $z\sim 2 $ and compare our
results to the TNG100 run of the IllustrisTNG cosmological simulation suite. In
the observations, we find that massive proto-cluster galaxies ($\log[{\rm
M}_{\ast}/{\rm M}_{\odot}]>$10.5) form $45 \pm 8 \%$ of their total stellar
mass in the first $2$ Gyr of the Universe compared to $31 \pm 2 \%$ formed in
the field galaxies. In both observations and simulations, massive proto-cluster
galaxies have a flat/declining SFH with decreasing redshift compared to rising
SFH in their field counterparts. Using IllustrisTNG, we find that massive
galaxies ($\log[{\rm M}_{\ast}/{\rm M}_{\odot}] \geq 10.5$) in both
environments are on average $\approx190$ Myr older than low mass galaxies
($\log[{\rm M}_{\ast}/{\rm M}_{\odot}]= 9-9.5$). However, the difference in
mean stellar ages of cluster and field galaxies is minimal when considering the
full range in stellar mass ($\log[{\rm M}_{\ast}/{\rm M}_{\odot}] \geq 9$). We
explore the role of mergers in driving the SFH in IllustrisTNG and find that
massive cluster galaxies consistently experience mergers with low gas fraction
compared to other galaxies after 1 Gyr from the Big Bang. We hypothesize that
the low gas fraction in the progenitors of massive cluster galaxies is
responsible for the reduced star formation.
