Observations show that the expansion of the Universe is accelerating.This requires that the dominant constituent ofmatter in the Universe has some unusual properties like negativepressure. This exotic component has been given the namedark energy. We work with the simplest model of dark energy,the cosmological constant introduced by Einstein. Westudy the evolution of spherical over-densities in such a modeland show that there is a minimum over-density required forcollapse; perturbations with a smaller amplitude do not collapse.This threshold is interesting as even perturbations witha positive over-density and negative energy do not collapse infinite time. Further, we show that perturbations with an amplitudelarger than, but comparable to the threshold value,take a very long time to collapse. We compare the solutionswith the case when dark energy is absent.