Gödel-type universes in f(R) gravity

The f(R) gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a f(R) theory, a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the f(R) gravity theories permit space-times in which the causality is violated. We show that the field equations of these f(R) gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid Gödel-type solution of a generic f(R) gravity satisfying the condition df/dR>0 is necessarily isometric to the Gödel geometry, and therefore presents violation of causality. This result extends a theorem on Gödel-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius r_c (beyond which the causality is violated) for an arbitrary f(R) theory, making apparent that the violation of causality depends on both the f(R) gravity theory and the matter content. As an illustration, we concretely take a recent f(R) gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal Gödel-type solutions.