We suggest a novel picture of the quantum Universe—its creation is described through thedensity matrix defined by the Euclidean path integral. This yields an ensemble of universes—acosmological landscape—in a mixed state which is shown to be dynamically preferable tothe pure quantum state of the Hartle–Hawking type. The latter is dynamically suppressedby the infinitely large positive action of its instanton, generated by the conformal anomalyof quantum fields within the cosmological bootstrap (the self-consistent back-reaction ofhot matter). This bootstrap suggests a solution to the problem of boundednessof the on-shell cosmological action and eliminates the infrared catastrophe of asmall cosmological constant in Euclidean quantum gravity. The cosmologicallandscape turns out to be limited to a bounded range of the cosmological constantΛmin≤Λ≤Λmax. Thedomain Λ<Λmin is ruled out by the back-reaction effect which we analyse by solving effective Euclideanequations of motion. The upper cut-off is enforced by the quantum effects ofvacuum energy and the conformal anomaly mediated by a special ghost-avoidancerenormalization of the effective action. They establish a new quantum scaleΛmax which is determined by the coefficient of the topological Gauss–Bonnet term in theconformal anomaly. This scale is realized as the upper bound—the limiting point of aninfinite sequence of garland-type instantons which constitute the full cosmologicallandscape. The dependence of the cosmological constant range on particle phenomenologysuggests a possible dynamical selection mechanism for the landscape of string vacua.