Noether Symmetries as a geometric criterion to select theories of gravity

TL;DR

This paper reviews the Noether Symmetry Approach as a geometric method to select and solve gravity theories, constraining functions in the action and finding exact solutions in cosmological models.

Contribution

It introduces the use of Noether Symmetries as a criterion for selecting and solving gravity theories, providing a systematic way to find solutions and constrain model functions.

Findings

Identifies exact solutions in cosmological models using Noether Symmetries.

Demonstrates how to constrain arbitrary functions in gravity actions.

Shows the effectiveness of the approach in solving field equations.

Abstract

We review the {\it Noether Symmetry Approach} as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.