Analysis of the non-minimally coupled scalar field in the Palatini formalism by the Noether symmetry approach

TL;DR

This paper investigates a non-minimally coupled scalar field in a flat universe using the Palatini formalism and Noether symmetry, deriving solutions relevant for dark energy modeling.

Contribution

It introduces a novel application of Noether symmetry to constrain the scalar field coupling and potential within the Palatini formalism in cosmology.

Findings

Massive scalar field linked to a Noether symmetry.

Analytical solutions for scalar field cosmology derived.

Implications for dark energy description discussed.

Abstract

We analyse a scalar field non-minimally coupled to gravity in the context of a Universe described by the flat Friedmann-Robertson-Walker (F-R-W) metric. The adopted model comprises a Universe filled by the scalar field and standard matter (dark and baryonic). The corresponding field equations are obtained through the Palatini formalism. From the action of the model in the flat F-R-W space-time, a point-like Lagrangian of first order is obtained and the Noether symmetry approach is applied to restrict the forms of the a priori undefined coupling and potential of the scalar field. We show that the massive scalar field is associated with a Noether symmetry of the model. Analytical cosmological solutions for this case are found and their respective importance for the description of the dark energy are discussed.