Novel aspects of C-theories in Cosmology
  The field equations in FRW background for the so called C-theories are
presented and investigated. In these theories the usual Ricci scalar is
substituted with $f(\mathcal{R})$ where $\mathcal{R}$ is a Ricci scalar related
to a conformally scaled metric $\hat{g}_{\mu\nu} =
\mathcal{C}(\mathcal{R})g_{\mu\nu}$, where the conformal factor itself depends
on $\mathcal{R}$. It is shown that homogeneous perturbations of this Ricci
scalar around general relativity FRW background of a large class of these
theories are either inconsistent or unstable.
