  We have investigated the emerging conformal field theory behavior on the
interior interface of the region near the cosmological event horizon on an
example of massless Dirac fermions. Indeed, we have constructed and verified
the emerging de Sitter/CFT correspondence for the near cosmological event
horizon region.
  It is in this near horizon region where the infinitely thin shell of matter
with the stiffest equation of state (Zeldovich's matter) is placed in the model
for a thermodynamically stable `would be black hole' which is sometimes called
a gravastar or a dark energy star. We put forward the hypothesis to the effect
that the Zeldovich matter consists of the strongly correlated quanta which are
best described by the emerging conformal field theory in the near `would be
horizon' region of a gravastar/dark energy star.
