Is mimetic gravity a good (quantized geometry*) solution of the cosmological dark sector dynamics problem?

Lifting the veil of darkness surrounding the scalar sector of gravitation

Mimetic gravity has emerged as an interesting alternative to general relativity. Within this theory, the additional degree of freedom which mimics dark matter on cosmological scales emerges through a singular disformal transformation by means of which the conformal degree of freedom of gravity is isolated in a covariant way. Various works have previously investigated background cosmological solutions in mimetic gravity, finding that appropriate choices of the potential for the mimetic field lead to appealing cosmological solutions, which can reproduce expansion histories in agreement with observational data without the need for additional dark matter or dark energy fluids.

In this work we have performed a dynamical-systems analysis of mimetic gravity, which has allowed us to study the cosmological dynamics of the theory. We have focused on both general potentials for the mimetic field, as well as on a set of well-motivated specific choices.

From the point of view of the expansionary history, our analysis suggests that the potential whose solutions are most appealing is the inverse square potential. The corresponding solutions possess an early-time radiation phase, followed successively by matter era and late-time accelerating scaling solution, which can alleviate the coincidence problem. We mention that this alleviation of the coincidence problem is obtained without imposing an interaction between dark-matter and dark-energy sectors by hand, as it is the usual approach [133], but it arises from the scenario of mimetic gravity itself. Therefore, with this choice of potential, mimetic gravity is in agreement with observations, and it provides the correct phenomenology at early times, as opposed to simpler scalar-field models of dark energy where a stiff-matter dominated early-time solution is usually attained. Moreover, it should be remarked that the inverse square potential is also very well motivated from a high-energy ultraviolet completion point of view, aside from being renormalizable, which lends even more to the attractiveness of the model.

... in our work we have shown that the cosmological dynamics of mimetic gravity renders the theory a viable and interesting candidate to explain the universe’s history. At the same time, it is important and timely to go beyond the background analysis and analyze and understand structure formation within this scenario, as well as provide a full Markov Chain Monte Carlo analysis, comparing the model with observational data. It will also be important to confirm or discard the raised issues concerning instabilities, in order to ascertain whether or not the theory of mimetic gravity is really viable. We leave these issues to future projects.

Cosmological dynamics of mimetic gravity

Jibitesh Dutta, Wompherdeiki Khyllep, Emmanuel N. Saridakis, Nicola Tamanini, Sunny Vagnozzi

(Submitted on 20 Nov 2017)

*edited on December 12 2017

To uncover how a possible quantization of geometry leads naturally to mimetic gravity the reader is invited to get a summary from the conclusion of this review article (which title may sound awkward from a physicist point of view but the substance of which offers fascinating physical perspective).