Noether gauge symmetry for $f(R)$ gravity in Palatini formalism

TL;DR

This paper uses Noether gauge symmetry to determine the form of $f(R)$ gravity in Palatini formalism, deriving exact solutions that describe power-law cosmic expansion in a flat FRW universe.

Contribution

It introduces a method to find specific $f(R)$ models in Palatini formalism using symmetry principles, leading to exact cosmological solutions.

Findings

Derived the form of $f(R)$ yielding power-law expansion.

Obtained exact solutions for the cosmic scale factor.

Demonstrated the applicability of Noether gauge symmetry in Palatini $f(R)$ gravity.

Abstract

In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini $f(R)$ theory of gravity. Using the dynamical equivalence between $f(R)$ gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying {\em Noether gauge symmetry approach} for this $f(R)$ Lagrangian we find out the form of $f(R)$ and the exact solution for cosmic scale factor. It is shown that the resulting form of $f(R)$ yield a power-law expansion for the scale factor of the universe.