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Generalized energy conditions in Extended Theories of Gravity

Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that causality is preserved and that "plausible" physical sources have been considered. 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 perfect fluids that carry different meanings 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, as the latter contains the matter content and a geometrical quantity, which arises from the ETG considered. Here, we explore this subtlety, extending on 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 non-conservation of the energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs, such as scalar-tensor gravity, $f(R)$ gravity and modified Gauss-Bonnet gravity. Interesting results appear such as matter that may exhibit unusual thermodynamical features, for instance, and gravity that retains its attractive character in the presence of negative pressures; or alternatively, we verify that repulsive gravity may occur for standard matter.