Using Noether symmetries to specify f(R) gravity

Abstract

A detailed study of the modified gravity, f(R) models is performed, using the fact that the Noether point symmetries of these models are geometric symmetries of the mini su-perspace 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 (Rb − 2Λ)c model, which generalizes the Lambda Cosmology. Furthermore using the corresponding Noether integrals we compute the analytic form of the main cosmological functions.