What Casimir Energy can suggest about Space Time Foam?

In the context of a model of space-time foam, made by $N$ wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground state of the foamy type.Comment: ReVTeX, 3 pages. Talk given at the Fifth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, September 10-14, 200

Traversable Wormholes in Distorted Gravity

We consider the effects of Distorted Gravity on the traversability of the wormholes. In particular, we consider configurations which are sustained by their own gravitational quantum fluctuations. The Ultra-Violet divergences appearing to one loop are taken under control with the help of a Noncommutative geometry representation and Gravity's Rainbow. In this context, it will be shown that for every framework, the self-sustained equation will produce a Wheeler wormhole, namely a wormhole of Planckian size. This means that, from the point of view of traversability, the wormhole will be traversable in principle, but not in practice. To this purpose, in the context of Gravity's Rainbow we have considered different proposals of rainbow's functions to see if the smallness of the wormhole is dependent on the chosen form of the rainbow's function. Unfortunately, we discover that this is not the case and we suggest that the self-sustained equation can be improved to see if the wormhole radius can be enlarged or not. Some consequences on topology change are discussed.Comment: 12 pages, to appear in a special volume of the IJMPD, dedicated to the VII Black Holes Workshop, Aveiro, Portugal, 18-19 December 201

The cosmological constant as an eigenvalue of the Hamiltonian constraint in Horava-Lifshits theory

In the framework of Horava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed with the help of a variational procedure with trial wave functionals of the Gaussian type. We analyze both the case with the detailed balanced condition and the case without it. In the case without the detailed balance, we find the existence of an eigenvalue depending on the set of coupling constants (g2,g3) and (g4,g5,g6), respectively, and on the physical scale.Comment: RevTeX,11 Pages, Substantial Improvements. References added. To appear in Phys.Rev.