Spacetime Foam and Vacuum Energy

The term Spacetime Foam was introduced for the first time by J.A. Wheeler at the end of the fifties to indicate that quantum fluctuations come into play at the Planckian scale, changing topology and metric [1]. Apart the pioneering path integral approach to Spacetime Foam, considered by S.W. Hawking [2], only recently the subject has been widely reconsidered in the context of brane physics [3], spin foam models [4] and on a phenomenological ground [5]. We will briefly introduce a different approach based on a large Nw-wormhole semi-classical approximation. This model is motivated by the results on the computation of the Casimir energy computed on some wormhole backgrounds of spherical symmetry (Schwarzschild, Schwarzschild-de Sitter, Schwarzschild-Anti-de Sitter and Reissner-Nordström metrics) which have as a reference space the presumed ground state (Minkowski, de Sitter and Anti-de Sitter metrics) [6, 7, 8, 9]. The formulation of the Casimir effect in general is synthesized by the Eq. ECasimir [∂M] = E0 [∂M]− E0 [0] , (1)