f(R) cosmology by Noether's symmetry

TL;DR

This paper presents a method to find exact cosmological solutions in f(R)-gravity by using Noether symmetries, which helps identify viable models and solve equations of motion.

Contribution

It introduces a symmetry-based approach to select and solve f(R) gravity models without relying solely on phenomenological assumptions.

Findings

Identifies specific f(R) models with Noether symmetries.

Provides exact solutions to cosmological equations in these models.

Offers criteria for solutions even without Noether charges.

Abstract

A general approach to find out exact cosmological solutions in f(R)-gravity is discussed. Instead of taking into account phenomenological models, we assume, as a physical criterium, the existence of Noether symmetries in the cosmological f(R) Lagrangian. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We discuss also the case in which no Noether charge is present but general criteria can be used to achieve solutions.