Thermodynamics via creation from nothing: Limiting the cosmological constant landscape

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 ${\Lambda }_{\min }\le \Lambda \le {\Lambda }_{\max }$. The domain $\Lambda <{\Lambda }_{\min }$ 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 ${\Lambda }_{\max }$ 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.

Figure 1

Density matrix instanton. Dashed lines depict the Lorentzian Universe nucleating at minimal surfaces $\Sigma$ and ${\Sigma }^{\prime }$.

Figure 2

Density matrix of the pure Hartle-Hawking state represented by the union of two vacuum instantons.

Figure 3

Instanton domain in the $(H^2,C)$-plane. Garland families are shown for $k=1$, 2, 3, 4. Their sequence accumulates at the critical point $(1/2B,B/2)$.

Figure 4

The garland segment consisting of three folds of a simple instanton glued at surfaces of a maximal scale factor.