Abstract:
Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation,
wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework,
it is possible to provide a unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a
very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal
formulation of the model. We devote particular focus to the reconstruction technique, which allows the realization of any desired
expansionary history of the universe by an accurate choice of potential or other functions defined within the theory (as in the case
of mimetic 𝑓(𝑅) gravity). We briefly discuss cosmological perturbation theory within mimetic gravity. As a case study within which
we apply the concepts previously discussed, we study a mimetic Hoˇrava-like theory, of which we explore solutions and cosmological
perturbations in detail. Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity
and apply our findings to the problem of galactic rotation curves. Our review provides an introduction to mimetic gravity, as well
as a concise but self-contained summary of recent findings, progress, open questions, and outlooks on future research directions.
