Covariant formalism and Noether symmetries on scalar-field cosmologies

Abstract

In this work, we investigate a cosmological model in the context of the covariant formalism proposed by Canuto et al. where the notion of atomic and gravitational units is invoked. We consider a minimally coupled scalar field as gravitational source, including a self-interacting potential. It is possible to determine the symmetries associated to the correspondent field theory using the Noether procedure, through the Lie derivative construction. This permits to determine the scale function [Formula: see text], present in the covariant formalism, that maps the physics between descriptions in atomic and gravitational units. In gravitational units it is verified that the Klein–Gordon field behaves as a dark constituent. On the other hand, in atomic units what emerges is an initially accelerated universe, with a later incursion into a decelerated one, mirroring the usual matter/radiation age.