Vacuum and semiclassical gravity: a difficulty and its bewildering significance

Abstract

We review a long-standing difficulty in some semiclassical models of vacuum and vacuum decay. Surprisingly enough these models, careless of their transparent formulation, are affected by, both, technical and conceptual issues. After proving some general results that are relevant for, both, the Euclidean and Lorentzian sectors of their dynamics, we briefly highlight their importance in connection with the issues discussed before, arguing that their solution might be interesting in our quest for quantum gravity.