Functional Schroedinger picture for conformally flat spacetime with cosmological constant

TL;DR

This paper develops a quantum-field model for conformally flat spacetime with a cosmological constant, interpreting the conformal factor as an inflaton field and analyzing its quantum properties and classical limit.

Contribution

It introduces a novel quantum-field formulation of conformally flat spacetime with a negative kinetic term, linking the conformal factor to inflationary dynamics.

Findings

Conformal factor acts as an inflaton field.

Quantum quanta of the model have negative energy.

Vacuum state corresponds to classical flat Friedmann Universe.

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.