Conformal fields and the quantum state of the universe

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 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. A correspondence between the 4-dimensional modified quantum Freidmann equations and the Friedmann equations arising in the context of 5-dimensional classical cosmological models was established.