f(R) as a dark energy fluid
  We study the equations for the evolution of cosmological perturbations in
$f\left(\mathcal{R}\right)$ and conclude that this modified gravity model can
be expressed as a dark energy fluid at background and linearised perturbation
order. By eliminating the extra scalar degree of freedom known to be present in
such theories, we are able to characterise the evolution of the perturbations
in the scalar sector in terms of equations of state for the entropy
perturbation and anisotropic stress which are written in terms of the density
and velocity perturbations of the dark energy fluid and those in the matter, or
the metric perturbations. We also do the same in the much simpler vector and
tensor sectors. In order to illustrate the simplicity of this formulation, we
numerically evolve perturbations in a small number of cases.
