On Shear-free perturbations of f(R) gravity

TL;DR

This paper explores shear-free perturbations in f(R) gravity, revealing conditions where properties similar to Newtonian physics emerge, contrasting with traditional General Relativity predictions.

Contribution

It generalizes shear-free perturbation results from GR to f(R) gravity, identifying scenarios where Newtonian-like behavior appears in modified gravity.

Findings

Existence of shear-free scenarios avoiding previous constraints

f(R) gravity can mimic Newtonian properties not seen in GR

Potential implications for cosmological models

Abstract

Recently it was shown that if the matter congruence of a general relativistic perfect fluid flow in an almost FLRW universe is shear-free, then it must be either expansion or rotation-free. Here we generalize this result for a general f(R) theory of gravity and show there exist scenarios where this result can be avoided. This suggests that there are situations where linearized forth-order gravity shares properties with Newtonian theory not valid in General Relativity.