Palatini f(R) gravity and Noether symmetry

TL;DR

This paper uses Noether symmetry to analyze Palatini f(R) gravity in cosmology, identifying specific forms of f(R) that admit symmetries and deriving exact solutions for the universe's expansion.

Contribution

It demonstrates that Noether symmetry exists for f(R) proportional to R^n in Palatini formalism, providing a method to determine f(R) and solutions for cosmic evolution.

Findings

Noether symmetry exists for f(R) ~ R^n

Exact solutions for the scale factor are obtained

The Noether constant relates to gravitational and matter parameters

Abstract

We study Palatini f(R) cosmology using Noether symmetry approach for the matter dominated universe. In order to construct a point-like Lagrangian in the flat FRW space time, we use the dynamical equivalence between f(R) gravity and scalar-tensor theories. The existence of Noether symmetry of the cosmological f(R) Lagrangian helps us to find out the form of f(R) and the exact solutions for cosmic scale factor. We show that this symmetry always exist for f(R)~R^n and the Noether constant is a function of the Newton's gravitational constant and the current matter content of the universe.