Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics

TL;DR

Mimetic gravity extends General Relativity to unify explanations for dark matter, dark energy, and inflation, with recent developments focusing on reconstruction techniques, cosmological perturbations, and astrophysical applications.

Contribution

This review summarizes recent advances in mimetic gravity, including its extensions, reconstruction methods, perturbation theory, and applications to cosmology and astrophysics.

Findings

Reconstruction technique enables modeling any desired cosmic expansion history.

Mimetic gravity can mimic dark matter and explain galactic rotation curves.

Analysis of cosmological perturbations within mimetic frameworks.

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 an 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 Ho\v{r}ava-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, progresses, open questions, and outlooks on future research directions.