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We explore a model in which the cosmological constant $\Lambda$ and thedensity contrast at the time of recombination $\sigma_{rec}$ are randomvariables, whose range and {\it a priori} probabilities are determined by thelaws of physics. (Such models arise naturally in the framework of inflationarycosmology.) Based on the assumption that we are typical observers, we show thatthe order of magnitude coincidence among the three timescales: the time ofgalaxy formation, the time when the cosmological constant starts to dominatethe cosmic energy density, and the present age of the universe, finds a naturalexplanation. We also discuss the probability distribution for $\sigma_{rec}$,and find that it is peaked near the observationally suggested values, for awide class of {\it a priori} distributions.Comment: 26 pages RevTeX, 5 figure

Cosmological constant and the time of its dominance