  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.
