Tunneling geometries: Analyticity, unitarity, and instantons in quantum cosmology
Abstract
We present the theory of tunneling geometries, which describes in the language of analytic continuation the nucleation of the Lorentzian universe from the Euclidean spacetime. We reformulate the underlying noboundary wave function in the manifestly unitary representation of true physical variables and calculate it in the oneloop approximation. For this purpose a special technique of complex extremals is developed, which reduces the formalism of complex tunneling geometries to real ones, and also the method of collective variables is applied, separating the macroscopic degrees of freedom from the perturbative microscopic modes. The quantum distribution of Lorentzian universes on the space of collective variables incorporates the probability conservation and boils down to the partition function of quaside Sitter gravitational instantons weighted by their Euclidean effective action. The overPlanckian behavior of their distribution is determined by the anomalous scaling of the theory, which serves as a criterion for the highenergy normalizability 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 establish a sound link between quantum cosmology, inflation theory, and particle physics in the model with a nonminimally coupled inflaton field.
 Publication:

Physical Review D
 Pub Date:
 October 1994
 DOI:
 10.1103/PhysRevD.50.5093
 arXiv:
 arXiv:grqc/9311022
 Bibcode:
 1994PhRvD..50.5093B
 Keywords:

 04.60.Ds;
 04.62.+v;
 98.80.Hw;
 Canonical quantization;
 Quantum field theory in curved spacetime;
 General Relativity and Quantum Cosmology
 EPrint:
 78 pages, latex, figures are not included (available on request by regular mail), report Alberta Thy4093