Generalized energy conditions in extended theories of gravity

In this work, we consider the further degrees of freedom related to curvature invariants and scalar fields in extended theories of gravity (ETG). These new degrees of freedom can be recast as effective fluids that differ in nature with respect to the standard matter fluids generally adopted as sources of the field equations. It is, thus, somewhat misleading to apply the standard general relativistic energy conditions to this effective energy-momentum tensor, as the latter contains the matter content and a geometrical quantity, which arises from the specific ETG considered. Here we explore this subtlety, extending our previous work, in particular, to cases with the contracted Bianchi identities with diffeomorphism invariance and to cases with generalized explicit curvature-matter couplings, which imply the nonconservation of the energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs, such as scalar-tensor gravity and f(R) gravity. Thus, in the context of ETGs, interesting results appear such as matter that may exhibit unusual thermodynamical features, for instance, gravity that retains its attractive character in the presence of large negative pressures; or alternatively, we verify that repulsive gravity may occur for standard matter.