Irrotational-fluid cosmologies in fourth-order gravity

In this paper, we explore classes of irrotational-fluid cosmological models in the context of f®-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f® gravitational Lagrangian. In particular, we investigate the consistency of linearised dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-elecric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in f®-gravity.