Cosmological Tests of Gravity

Cosmological observations are beginning to reach a level of precision that allows us to test some of the most fundamental assumptions in our working model of the Universe. One such assumption is that gravity is governed by the theory of general relativity. In this review, we discuss how one might go about extending general relativity and how such extensions can be described in a unified way on large scales. This allows us to describe the phenomenology of modified gravity in the growth and morphology of the large-scale structure of the Universe. On smaller scales, we explore the physics of gravitational screening and how it might manifest itself in galaxies, clusters, and, more generally, in the cosmic web. We then analyze the current constraints from large-scale structure and conclude by discussing the future prospects of the field in light of the plethora of surveys currently being planned. Key results include the following: There are a plethora of alternative theories of gravity that are restricted by fundamental physics considerations. There is now a well-established formalism for describing cosmological perturbations in the linear regime for general theories of gravity. Gravitational screening can mask modifications to general relativity on small scales but may, itself, lead to distinctive signatures in the large-scale structure of the Universe. Current constraints on both linear and nonlinear scales may be affected by systematic uncertainties that limit our ability to rule out alternatives to general relativity. The next generation of cosmological surveys will dramatically improve constraints on general relativity, by up to two orders of magnitude.