Gravitational collapse and structure formation in an expanding universe
  with dark energy
  Observations show that the expansion of the Universe is accelerating. This
requires that the dominant constituent of matter in the Universe has some
unusual properties like negative pressure. This exotic component has been given
the name dark energy. We work with the simplest model of dark energy, the
cosmological constant introduced by Einstein. We study the evolution of
spherical over-densities in such a model and show that there is a minimum
over-density required for collapse: perturbations with a smaller amplitude do
not collapse. This threshold is interesting as even perturbations with a
positive over-density and negative energy do not collapse in finite time.
Further, we show that perturbations with an amplitude larger than, but
comparable to the threshold value, take a very long time to collapse. We
compare the solutions with the case when dark energy is absent.
