Black hole formation in a contracting universe
  We study the evolution of cosmological perturbations in a contracting
universe. We aim to determine under which conditions density perturbations grow
to form large inhomogeneities and collapse into black holes. Our method
consists in solving the cosmological perturbation equations in complete
generality for a hydrodynamical fluid. We then describe the evolution of the
fluctuations over the different length scales of interest and as a function of
the equation of state for the fluid, and we explore two different types of
initial conditions: quantum vacuum and thermal fluctuations. We also derive a
general requirement for black hole collapse on sub-Hubble scales, and we use
the Press-Schechter formalism to describe the black hole formation probability.
For a fluid with a small sound speed (e.g., dust), we find that both quantum
and thermal initial fluctuations grow in a contracting universe, and the
largest inhomogeneities that first collapse into black holes are of Hubble size
and the collapse occurs well before reaching the Planck scale. For a
radiation-dominated fluid, we find that no black hole can form before reaching
the Planck scale. In the context of matter bounce cosmology, it thus appears
that only models in which a radiation-dominated era begins early in the
cosmological evolution are robust against the formation of black holes. Yet,
the formation of black holes might be an interesting feature for other models.
We comment on a number of possible alternative early universe scenarios that
could take advantage of this feature.
