Classical and semi-classical analysis of Klein-Gordon field in a signature transition spacetime

Classical and semiclassical analyses of a Klein-Gordon field minimally coupled to a fixed, signature-changing (Riemannian to Lorentzian) background are performed. The background spacetime is a toy model used to represent a possible history considered in the Hartle-Hawking no boundary proposal. An extensive study is given of matching techniques to allow continuation of the Klein-Gordon field through the change of signature. The classical analysis focuses on exploring the consequences of imposing regularity conditions on the field in the Riemannian sector. The semiclassical analysis investigates the particle production due to gravitational interaction, assuming that when the universe tunnels into existence, the Klein-Gordon field is in the minimum energy vacuum state. It is found that the particle production rate is nonzero at large wavenumber k, and that the rate of production decreases as k⁻².