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.
