Rapid early coeval star formation and assembly of the most massive
  galaxies in the universe
  The current consensus on the formation and evolution of the brightest cluster
galaxies is that their stellar mass forms early ($z \gtrsim 4$) in separate
galaxies that then eventually assemble the main structure at late times ($z
\lesssim 1$). However, advances in observational techniques have led to the
discovery of protoclusters out to $z \sim 7$, suggesting that the late-assembly
picture may not be fully complete. If these protoclusters assemble rapidly in
the early universe, they should form the brightest cluster galaxies much
earlier than suspected by the late-assembly picture. Using a combination of
observationally constrained hydrodynamical and dark-matter-only simulations, we
show that the stellar assembly time of a sub-set of the brightest cluster
galaxies occurs at high redshifts ($z > 3$) rather than at low redshifts ($z <
1$), as is commonly thought. We find, using isolated non-cosmological
hydrodynamical simulations, that highly overdense protoclusters assemble their
stellar mass into brightest cluster galaxies within $\sim 1$ $\mathrm{Gyr}$ of
evolution -- producing massive blue elliptical galaxies at high redshifts ($z
\gtrsim 1.5$). We argue that there is a downsizing effect on the cluster scale
wherein some of the brightest cluster galaxies in the cores of the most-massive
clusters assemble earlier than those in lower-mass clusters. In those clusters
with $z = 0$ virial mass $\geqslant 5\times10^{14}$ M$_\mathrm{\odot}$, we find
that $9.8$% have their cores assembly early, and a higher fraction of $16.4$%
in those clusters above $10^{15}$ M$_\mathrm{\odot}$. The James Webb Space
Telescope will be able to detect and confirm our prediction in the near future,
and we discuss the implications to constraining the value of
$\sigma_\mathrm{8}$.
