Equivalence of non-minimally coupled cosmologies by Noether symmetries

TL;DR

This paper demonstrates that non-minimally coupled cosmological models involving various geometric invariants are dynamically equivalent if they share the same Noether symmetries, which serve as a criterion for comparing different gravity theories.

Contribution

It shows that Noether symmetries determine couplings and potentials in non-minimally coupled cosmologies and establish their dynamical equivalence across different geometric invariants.

Findings

Different theories with the same Noether symmetries are dynamically equivalent.

Noether symmetries can be used to select and compare gravity theories.

The approach simplifies solving the dynamics of complex cosmological models.

Abstract

We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different non-minimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are a selection criterion to compare different theories of gravity.