Simultaneous expansion and rotation of shear-free universes in modified
  gravity

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Abstract

We show in a fully covariant way that, there exist a class of \(f(R)\) models for which a shear-free, almost FLRW universe can expand and rotate at the same time .

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Is Open Access

On Shear-free perturbations of f(R) gravity

Rituparno Goswami, Peter Dunsby (2011)

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.