Cosmological constant and the time of its dominance

We explore a model in which the cosmological constant $\Lambda$ and the density contrast at the time of recombination ${\sigma }_{\mathrm{rec}}$ are random variables, whose range and a priori probabilities are determined by the laws of physics. (Such models arise naturally in the framework of inflationary cosmology.) Based on the assumption that we are typical observers, we show that the order of magnitude coincidence among the three time scales, the time of galaxy formation, the time when the cosmological constant starts to dominate the cosmic energy density, and the present age of the universe, finds a natural explanation. We also discuss the probability distribution for ${\sigma }_{\mathrm{rec}}.$ Assuming a power law a priori distribution $\propto {\sigma }_{\mathrm{rec}}^{-\alpha }$ we find that for $\alpha >3\mathrm{}$ the most probable values of ${\sigma }_{\mathrm{rec}}$ are near the observationally suggested values, whereas for $\alpha <3\mathrm{}$ the typical ${\sigma }_{\mathrm{rec}}$ would be too large. This may be used to place constraints on inflationary models (or on any alternative theory of initial conditions).