Wormholes in Simplicial Minisuperspace

We consider a simplicial minisuperspace modelling wormhole configurations. Such configurations result from a cut and paste procedure on two identical copies of the most relevant triangulation of our universe, namely the cone over α4, which is the simplest triangulation of S. The connecting space where the two copies are glued, acts as the throat of a wormhole connecting two distinct universes. We show that the model contains both Euclidean and Lorentzian classical configurations, although the Euclidean configurations are restricted to very small size, while the Lorentzian ones exist for all sizes. By computing the steepest descents contours associated with the different kind of configurations, and studying the behaviour of the Euclidean action along these contours we are able to conclude that except for a very small range of boundary data, the semiclassical approximation is always valid, which facilitates both the computation and interpretation of the wavefunctions associated to those steepest descents contours. Having computed these semiclassical wavefunctions we could observe that in the case of the microscopic Euclidean wormhole configurations there is a strong prediction of a finite throat, which seems to indicate that such configurations are very likely. For large universe there are only Lorentzian configurations. Some of them have fully complex Euclidean action and the exp(−ReI) acts as the weighting of the Lorentzian e-mail address : clbc2@damtp.cam.ac.uk e-mail address : rmw7@damtp.cam.ac.uk configurations. We find large universes connected by similarly large throats to be strongly favoured.