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Observations show that the expansion of the Universe is accelerating. Thisrequires that the dominant constituent of matter in the Universe has someunusual properties like negative pressure. This exotic component has been giventhe name dark energy. We work with the simplest model of dark energy, thecosmological constant introduced by Einstein. We study the evolution ofspherical over-densities in such a model and show that there is a minimumover-density required for collapse: perturbations with a smaller amplitude donot collapse. This threshold is interesting as even perturbations with apositive over-density and negative energy do not collapse in finite time.Further, we show that perturbations with an amplitude larger than, butcomparable to the threshold value, take a very long time to collapse. Wecompare the solutions with the case when dark energy is absent.

Gravitational collapse and structure formation in an expanding universe with dark energy