Enriched Phenomenology in Extended Palatini Theories

We show that extended theories of gravity with Lagrangian f(R,R_{μν}R^{μν}) in the Palatini formulation possess a phenomenology much richer than the simpler f(R) or f(R_{μν}R^{μν}) theories. In fact, we find that the scalars R and Q=R_{μν}R^{μν} can be written as algebraic functions of the energy density and pressure of the energy momentum tensor. In the simpler cases of f(R) or f(R_{μν}R^{μν}) theories, R and Q are just functions of the trace T of the energy-momentum tensor. As a result, in radiation dominated universes f(R) and f(R_{μν}R^{μν}) theories exhibit the same dynamics as general relativity with an effective cosmological constant. This is not the case of f(R,R_{μν}R^{μν}) models, in which R=R(ρ,P) and Q=Q(ρ,P) and, therefore, modified dynamics exists even for traceless sources.

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