2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/188437The creation of a quantum Universe is described by a {\em density matrix} which yields an ensemble of universes with the cosmological constant limited to a bounded range $Λ_{\rm min}\leq Λ\leq Λ_{\rm max}$. The domain $Λ<Λ_{\rm min}$ 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 $Λ_{\rm max}$ establishes a new quantum scale -- the accumulation point of an infinite sequence of garland-type instantons. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.RevTex, 4 pages, 4 figuresHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext