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 fourth-order gravity shares properties with Newtonian theory not valid in General Relativity.

• Received 15 August 2011

DOI:https://doi.org/10.1103/PhysRevD.84.124027