Anti-Newtonian cosmologies in f(R) gravity

In this paper, we investigate a class of perfect-fluid "anti-Newtonian" cosmological models in the context of f(R) gravity. In particular, we study the integrability conditions of such gravity models using covariant consistency analysis formalisms. We show that, unlike the results in General Relativity, anti-Newtonian cosmologies are not silent models and that they can exist subject to the solution of an integrability condition equation we derive. We also present the set of evolution equations governing the linear perturbations of matter, expansion and Ricci scalar for this class of models.