  In this paper, we explore classes of irrotational-fluid cosmological models
in the context of f(R)-gravity in an attempt to put some theoretical and
mathematical restrictions on the form of the f(R) 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(R)-gravity.
