Extended Theories of Gravity with Generalized Energy Conditions

TL;DR

This paper explores how energy conditions are modified in extended theories of gravity with scalar fields and curvature invariants, emphasizing the need for a broader interpretation beyond standard inequalities.

Contribution

It introduces a generalized framework for energy conditions in extended gravity theories, considering additional geometric degrees of freedom and their impact on gravitational attraction.

Findings

Standard energy inequalities may not guarantee gravity's attractiveness in extended theories.

Generalized energy conditions are necessary for consistent physical interpretations.

Curvature terms can be recast as effective energy-momentum contributions.

Abstract

We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical fluids} that differ in meaning with respect to the matter fluids generally considered as sources of the field equations. In extended gravity theories the curvature terms are encapsulated in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$ that can be recast as effective Einstein field equations, with corrections to the energy-momentum tensor of matter. The formal validity of standard energy inequalities does not assure basic requirements such as the attractive nature of gravity, so we argue that the energy conditions have to be considered in a wider sense.