We present an overview of a recently suggested new model of quantum initial conditions for the Universe in the form of a cosmological density matrix. This density matrix originally suggested in the Euclidean quantum gravity framework turns out to describe the microcanonical ensemble in the Lorentzian quantum gravity of spatially closed cosmological models. This ensemble represents an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry it is peaked about a set of cosmologies limited to a bounded range of the cosmological constant. This suggests a mechanism to constrain the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasi-equilibrium decay of the microcanonical state of the Universe. The effective Friedmann equation governing this decay incorporates the effect of the conformal anomaly of quantum fields and features a new mechanism for a cosmological acceleration stage -- big boost scenario. We also briefly discuss the relation between our model, the AdS/CFT correspondence and RS and DGP braneworlds.