  The 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 $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The
domain $\Lambda<\Lambda_{\rm min}$ 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 $\Lambda_{\rm
max}$ 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.
