The problem of initial conditions in cosmology

Abstract

The creation of a quantum Universe is described by a density matrix which yields an ensemble of universes with the cosmological constant limited to a bounded range Λmin⩽Λ⩽Λmax. The domain Λ<Λmin is ruled out by a cosmological bootstrap requirement (the self‐consistent back reaction of hot matter). The upper cutoff results from the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost‐avoidance renormalization. The cutoff Λmax establishes a new quantum scale—the accumulation point of an infinite sequence of garland‐type instantons. The Euclidean path integral formalism used for the construction of the fundamental density matrix for a mixed state of the Universe is justified by proving its correspondence to the microcanonical ensemble in quantum cosmology. The cosmological evolution starting with these initial conditions also have some new features: the stage of cosmic acceleration can be followed by a big boost singularity—a rapid growth up to infinity of the scale factor acceleration parameter. From the developed approach it follows that the notion of the density matrix plays a more fundamental role than that was traditionally prescribed to it.