Modifications of gravity

Abstract

General relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The deep mystery of dark energy (and possibly even the requirement of cold dark matter (CDM)) has increased the need for testing modifications to GR, as the inference of such otherwise undetected fluids depends crucially on the theory of gravity. Here, I discuss a general scheme for constructing consistent and covariant modifications to the Einstein equations. This framework is such that there is a clear connection between the modification and the underlying field content that produces it. I argue that this is mandatory for distinguishing modifications of gravity from conventional fluids. I give a non-trivial example, a simple metric-based modification of the fluctuation equations for which the background is exact Λ CDM, but differs from it in the perturbations. I show how this can be generalized and solved in terms of two arbitrary functions. Finally, I discuss future prospects and directions of research.