  We study the field equations of modified theories of gravity in which the
lagrangian is a general function of the Ricci scalar and Ricci-squared terms in
Palatini formalism. We show that the independent connection can be expressed as
the Levi-Civita connection of an auxiliary metric which, in particular cases of
interest, is related with the physical metric by means of a disformal
transformation. This relation between physical and auxiliary metric boils down
to a conformal transformation in the case of f(R) theories. We also show with
explicit models that the inclusion of Ricci squared terms in the action can
impose upper bounds on the accessible values of pressure and density, which
might have important consequences for the early time cosmology and black hole
formation scenarios. Our results indicate that the phenomenology of
f(R_{ab}R^{ab}) theories is much richer than that of f(R) and f(R_{ab}R^{ab})
theories and that they also share some similarities with Bekenstein's
relativistic theory of MOND.
