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The path integral over Euclidean geometries for the recently suggesteddensity matrix of the Universe is shown to describe a microcanonical ensemblein quantum cosmology. This ensemble corresponds to a uniform (weight one)distribution in phase space of true physical variables, but in terms of theobservable spacetime geometry it is peaked about complex saddle-points of the{\em Lorentzian} path integral. They are represented by the recently obtainedcosmological instantons limited to a bounded range of the cosmologicalconstant. Inflationary cosmologies generated by these instantons at late stagesof expansion undergo acceleration whose low-energy scale can be attained withinthe concept of dynamically evolving extra dimensions. Thus, together with thebounded range of the early cosmological constant, this cosmological ensemblesuggests the mechanism of constraining the landscape of string vacua and,simultaneously, a possible solution to the dark energy problem in the form ofthe quasi-equilibrium decay of the microcanonical state of the Universe.

Why there is something rather than nothing (out of everything)?