Cosmological Landscape From Nothing: Some Like It Hot

We suggest a novel picture of the quantum Universe -- its creation is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed state which is shown to be dynamically more preferable than the pure quantum state of the Hartle-Hawking type. The latter is dynamically suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum fields within the cosmological bootstrap (the self-consistent back reaction of hot matter). This bootstrap suggests a solution to the problem of boundedness of the on-shell cosmological action and eliminates the infrared catastrophe of small cosmological constant in Euclidean quantum gravity. The cosmological landscape turns out to be limited to a bounded range of the cosmological constant $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain $\Lambda<\Lambda_{\rm min}$ is ruled out by the back reaction effect which we analyze by solving effective Euclidean equations of motion. The upper cutoff is enforced by the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost-avoidance renormalization of the effective action. They establish a new quantum scale $\Lambda_{\rm max}$ which is determined by the coefficient of the topological Gauss-Bonnet term in the conformal anomaly. This scale is realized as the upper bound -- the limiting point of an infinite sequence of garland-type instantons which constitute the full cosmological landscape. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.