Gravity theories with local energy-momentum exchange: a closer look at Rastall-like gravity

Einstein's famous equivalence principle is certainly one of the most striking features of the gravitational interaction. In a strict reading, it states that the effects of gravity can be made to disappear $locally$ by a convenient choice of reference frame. As a consequence, no covariantly-defined gravitational force should exist and energy-momentum of all matter and interaction fields combined, with gravity $excluded$, should be locally conserved. Although elegant, this separate conservation law represents a strong constraint on the dynamics of a gravitating system and it is only logical to question its naturality and observational basis. This is the purpose of the present work. For concreteness sake, we analyze, in the context of metric theories of gravity, the simplest phenomenological model which allows for local energy-momentum exchange between the spacetime and matter/interaction fields while preserving the seemingly more natural principle of general covariance. This concrete model turns out to be a generalization of the socalled Rastall's theory, with one important advantage: criticisms made to the latter, which are often used to dismiss it as a viable or interesting model, do not apply to the former in a universe containing "dark" ingredients, such as ours -- a connection which seems to have been overlooked thus far. We conclude by exploring the consequences of our Rastall-like model to standard (astrophysical and cosmological) gravitational scenarios.