Using Noether symmetries to specify f(R) gravity

TL;DR

This paper uses Noether symmetries to identify specific f(R) gravity models that are mathematically integrable, providing exact solutions relevant for cosmology.

Contribution

It demonstrates that Noether point symmetries can select consistent f(R) models and derives explicit cosmological solutions for the integrable case.

Findings

Identifies the (R^b - 2Λ)^c model as the unique integrable f(R) model in FLRW spacetime.

Provides analytic expressions for cosmological functions in the selected model.

Shows that symmetry considerations can guide the choice of viable modified gravity models.

Abstract

A detailed study of the modified gravity, f(R) models is performed, using that the Noether point symmetries of these models are geometric symmetries of the mini superspace of the theory. It is shown that the requirement that the field equations admit Noether point symmetries selects definite models in a self-consistent way. As an application in Cosmology we consider the Friedman -Robertson-Walker spacetime and show that the only cosmological model which is integrable via Noether point symmetries is the $(R^{b}-2\Lambda) ^{c}$ model, which generalizes the Lambda Cosmology. Furthermore using the corresponding Noether integrals we compute the analytic form of the main cosmological functions.