Andrei Barvinski (Lebedev Physics Institute) Why is there something rather than nothing (out of everything)? The path integral over Euclidean geometries for the recently suggested density matrix of the Universe is shown to describe a microcanonical ensemble in quantum cosmology. This ensemble corresponds to a uniform (weight one) distribution in phase space of true physical variables, but in terms of the observable spacetime geometry it is peaked about complex saddle-points of the {\em Lorentzian} path integral. They are represented by the recently obtained cosmological instantons limited to a bounded range of the cosmological constant. The conformal rotation, circumventing the problem of unboundedness of the Euclidean gravitational action, incorporates a correct integration range over the lapse function in Lorentzian quantum gravity, which enforces the Hamiltonian constraint. Zero value of this constraint is the only restriction on the microcanonical distribution in quantum cosmology of {\em closed} models which do not have other freely specifiable conserved charges. Inflationary cosmologies generated by the cosmological instantons at late stages of expansion undergo acceleration whose low-energy scale can be attained within the concept of dynamically evolving extra dimensions. Thus, together with the bounded range of the early cosmological constant, this cosmological ensemble suggests the mechanism of constraining the landscape of string vacua and, simultaneously, a possible solution to the dark energy problem in the form of the quasi-equilibrium decay of the microcanonical state of the Universe. 04 26 2007, ISCAP Seminar Room Pupin 908, 2:00pm