Functional Schroedinger picture for conformally flat spacetime with cosmological constant

Abstract

A quantum-field model of the conformally flat space is formulated using a standard field-theoretical technique, a probability interpretation and a way to establish the classical limit. The starting point is the following: after conformal transformation of the Einstein -- Hilbert action, the conformal factor represents a scalar field with the negative kinetical term and the self-interaction inspired by the cosmological constant. (It has been found that quanta of such action have a negative value as a sequence of the negative energy.) The metric energy-momentum tensor of this scalar field is proportional to the Einstein tensor for the initial metric. Therefore, a vacuum state of the field is treated as a classical space. In such vacuum the zero mode is a scale factor of the flat Friedmann Universe. It is shown that conformal factor may be viewed as a an inflaton field, and its small non-homogeneities represent gauge invariant scalar metric perturbations.