  We present results from a new cosmological hydrodynamics simulation campaign
of protocluster (PC) regions, FOREVER22: FORmation and EVolution of galaxies in
Extremely-overdense Regions motivated by SSA22. The simulations cover a wide
range of cosmological scales using three different zoom set-ups in a parent
volume of $(714.2~\rm cMpc)^{3}$: PCR (Proto-Cluster Region; $V= (28.6~{\rm
cMpc})^{3} $, SPH particle mass, $m_{\rm{SPH}} = 4.1 \times 10^{6}~\rm
M_{\odot}$ and final redshift, $z_{\rm end}=2.0$), BCG (Brightest proto-Cluster
Galaxy; $V \sim (10~{\rm cMpc})^{3} $, $m_{\rm SPH} = 5.0\times10^{5}~\rm
M_{\odot}$ and $z_{\rm end}=4.0$ ), and First ( $V \sim (3~{\rm cMpc})^{3} $,
$m_{\rm SPH} = 7.9 \times 10^{3}~\rm M_{\odot}$ and $z_{\rm end}=9.5$) runs,
that allow to focus on different aspects of galaxy formation. In the PCR runs,
we follow 10 PCs, each harbouring 1 - 4 SMBHs with $M_{\rm BH} \ge 10^{9}~\rm
M_{\odot}$. One of the PC cores shows a spatially close arrangement of seven
starburst galaxies with ${\rm SFR} \gtrsim 100~\rm M_{\odot}~yr^{-1}$ each,
that are dust-obscured and would appear as submillimeter galaxies with flux
$\gtrsim 1~$ mJy at $1.1~ \rm mm$ in observations. The BCG runs show that the
total SFRs of haloes hosting BCGs are affected by AGN feedback, but exceed
$1000~\rm M_{\odot}~yr^{-1}$ at $z \lesssim 6$. The First runs resolve
mini-haloes hosting population (Pop) III stars and we show that, in PC regions,
the dominant stellar population changes from Pop III to Pop II at $z \gtrsim
20$, and the first galaxies with ${\rm SFR} \gtrsim 18~\rm M_{\odot}~yr^{-1}$
form at $z \sim 10$. These can be prime targets for future observations with
the James Webb Space Telescope. Our simulations successfully reproduce the
global star formation activities in observed PCs and suggest that PCs can
kickstart cosmic reionization.
