Consistent cosmological modifications to the Einstein equations

General relativity 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), has increased the need for testing modifications to general relativity, as the inference of such otherwise undetected fluids, depends crucially on the theory of gravity. In this work I outline 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 two nontrivial examples, the first of which is a simple metric-based modification of the fluctuation equations for which the background is exact ΛCDM and the second has a Dvali-Gabadadze-Porrati background but differs from it in the perturbations. I present their impact on observations of the cosmic microwave background radiation.