Reality Conditions in Nonperturbative Quantum Cosmology

TL;DR

This paper investigates the nonperturbative quantum cosmology of various models, linking complex path-integral contours with reality conditions, and explores how different conditions influence the physical interpretation and equivalence of quantum theories.

Contribution

It establishes a connection between complex contour choices and reality conditions in quantum cosmology, showing their impact on wave function normalizability and theory equivalence.

Findings

Path integral contours relate to reality conditions for well-defined metrics.

Most wave functions are non-normalizable and not proper quantum states.

Different reality conditions can produce equivalent quantum theories.

Abstract

We carry out the nonperturbative canonical quantization of several types of cosmological models that have already been studied in the geometrodynamic formulation using the complex path-integral approach. We establish a relation between the choices of complex contours in the path integral and the sets of reality conditions for which the metric representation is well defined, proving that the ambiguity in the selection of complex contours disappears when one imposes suitable reality conditions. In most of the cases, the wave functions defined by means of the path integral turn out to be non-normalizable and cannot be accepted as proper quantum states. Moreover, the wave functions of the Universe picked out in quantum cosmology by the no-boundary condition and the tunneling proposals do not belong, in general, to the Hilbert space of quantum states. Finally, we show that different sets of reality conditions can lead to equivalent quantum theories. This fact enables us to extract physical predictions corresponding to Lorentzian gravity from quantum theories constructed with other than Lorentzian reality conditions.