TUNNELING GEOMETRIES - ANALYTICITY, UNITARITY, AND INSTANTONS IN QUANTUM COSMOLOGY

We present the theory of tunneling geometries, which describes in the language of analytic continuation the nucleation of the Lorentzian uni verse from the Euclidean spacetime. We reformulate the underlying no-b oundary wave function in the manifestly unitary representation of true physical variables and calculate it in the one-loop approximation. Fo r this purpose a special technique of complex extremals is developed,w hich reduces the formalism of complex tunneling geometries to real one s, and also the method of collective variables is applied, separating the macroscopic degrees of freedom from the perturbative microscopic m odes. The quantum distribution of Lorentzian universes on the space of collective variables incorporates the probability conservation and bo ils down to the partition function of quasi-de Sitter gravitational in stantons weighted by their Euclidean effective action. The over-Planck ian behavior of their distribution is determined by the anomalous scal ing of the theory, which serves as a criterion for the high-energy nor malizability of the cosmological wave function and the validity of the semiclassical expansion. It also provides a calculational scheme for obtaining the quantum scale of inflation which was recently shown to e stablish a sound link between quantum cosmology, inflation theory, and particle physics in the model with a nonminimally coupled inflaton fi eld.