KINEMATICS AND DYNAMICS OF F(R) THEORIES OF GRAVITY

We generalise the equations governing relativistic fluid dynamics give n by Ehlers and Ellis for general relativity, and by Maartens and Tayl or for quadratic theories, to generalised f(R) theories of gravity. In view of the usefulness of this alternative framework to general relat ivity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generali se, as an example, the results of Maartens and Taylor to show that wit hin the framework of general f(R) theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann-Lemaitre -Robertson-Walker only if the fluid has in addition a barotropic equat ion of state. It then follows that the Ehlers-Geren-Sachs theorem and its ''almost'' extension also hold for f(R) theories of gravity.