No-boundary wave function of the anti–de Sitter space-time and the quantization of Λ

The application of the “no-boundary” condition to space-times with initially open spatial sections may lead to extra conditions on physical quantities of these space-times. In the present Brief Report, we verify the above statement in a model where we compute the semi-classical approximation to the “no-boundary” wave function of the anti–de Sitter space-time. For this model the “no-boundary” conditions impose a well defined, discrete spectrum for the cosmological constant. As a by-product of our investigations we also find that among the space-times contributing to the above wave function there are two complex conjugate ones that show a new type of signature change.