An extreme proto-cluster of luminous dusty starbursts in the early
  Universe
  We report the identification of an extreme proto-cluster of galaxies in the
early Universe whose core (nicknamed Distant Red Core, DRC) is formed by at
least ten dusty star-forming galaxies (DSFGs), confirmed to lie at $z_{\rm
spec} = 4.002$ via detection of [CI](1-0), $^{12}$CO(6-5), $^{12}$CO(4-3),
$^{12}$CO(2-1) and ${\rm H_2O} (2_{11} - 2_{02})$ emission lines, detected
using ALMA and ATCA. The spectroscopically-confirmed components of the
proto-cluster are distributed over a ${\rm 260\, kpc \times 310\, kpc}$ region
and have a collective obscured star-formation rate (SFR) of $\sim 6500 \,
M_\odot \, {\rm yr}^{-1}$, considerably higher than has been seen before in any
proto-cluster of galaxies or over-densities of DSFGs at $z \gtrsim 4$. Most of
the star formation is taking place in luminous DSFGs since no Ly$\alpha$
emitters are detected in the proto-cluster core, apart from a Ly$\alpha$ blob
located next to one of the DRC dusty components and extending over $60\,{\rm
kpc}$. The total obscured SFR of the proto-cluster could rise to ${\rm SFR}
\sim 14,400 \, M_\odot \, {\rm yr}^{-1}$ if all the members of an over-density
of bright DSFGs discovered around DRC in a wide-field LABOCA 870-$\mu$m image
are part of the same structure. The total halo mass of DRC could be as high as
$\sim 4.4 \times 10^{13}\,M_\odot$ and could be the progenitor of a Coma-like
cluster at $z = 0$. The relatively short gas-depletion times of the DRC
components suggest either the presence of a mechanism able to trigger extreme
star formation simultaneously in galaxies spread over a few hundred kpc or the
presence of gas flows from the cosmic web able to sustain star formation over
several hundred million years.
