Partition Function for a Volume of Space

Axion flux monodromy discharges relax the cosmological constant

“…This realizes the old idea that the distribution of terminal values of the cosmological constant is controlled by the semiclassical Euclidean partition function of the theory [44,45]. Some recent works [46,47] provide new support for this idea.…”

Suppression of spacetime singularities in quantum gravity

“…An example for gravity is the Schwarzschild spacetime as solution to a quadraticgravity action S ϵ including in particular the Kretschmann scalar R µνρσ R µνρσ or the squared Weyl tensor C µνρσ C µνρσ , whose spacetime integral diverges as ϵ −3 in the limit ϵ → 0 where ϵ represents a regularizing small-distance cutoff. While partition functions for a fixed volume of space have been recently investigated based on the action of general relativity [80] and higher-derivative gravity [81], sheding light on the above question can be done by studying path integrals as function(al)s of variable or dynamical spatial boundary conditions, e.g. in our toy-model example Z(ϵ) ≡ Z(S ϵ ) with varying parameter ϵ. Alternatively, in the context of an analytical-mechanics system, one would have to investigate explicitly solutions with a divergent action resulting, e.g.…”

Lagrangian Partition Functions Subject to a Fixed Spatial Volume Constraint in the Lovelock Theory

“…where H ′ (x) is the first derivative of H with respect to its argument, and λ should be a pure constant since no factor is τ-dependent in the equation. Note that ( 16) imposes the same structure on h as in GR [17], which implies that the solutions for all Lovelock theories (GR included) are qualitatively the same. The only distinction between the various theories is that ( 14) admits multiple solutions that depend on the coupling constants α p .…”

“…Recently, Jacobson and Visser [17] considered some of these issues by adding a spatial volume constraint to the Euclidean path integral. They proposed a partition function with a Lagrange multiplier λ(τ) of the form…”

“…Together with the closedness in the τ direction, the desired saddle manifold should have a closed topology similar to the original Euclidean dS space. The partition function (1) was shown [17] to admit spherical saddle metrics of the form…”