Higher Derivative Mimetic Gravity

TL;DR

This paper explores how adding specific higher derivative terms to mimetic gravity stabilizes cosmological perturbations, enabling models like mimetic dark matter and nonsingular bounces, with potential links to loop quantum and Randall-Sundrum cosmologies.

Contribution

It introduces a classified set of higher derivative terms that stabilize mimetic perturbations and constructs new cosmological models including mimetic dark matter and nonsingular bounces.

Findings

Higher derivative terms remove instabilities in mimetic perturbations.

Constructed stable mimetic dark matter and bouncing cosmological scenarios.

Connected mimetic cosmology with loop quantum and Randall-Sundrum models.

Abstract

We study cosmological perturbations in mimetic gravity in the presence of classified higher derivative terms which can make the mimetic perturbations stable. We show that the quadratic higher derivative terms which are independent of curvature and the cubic higher derivative terms which come from curvature corrections are sufficient to remove instabilities in mimetic perturbations. The advantage of working with the classified higher derivative terms is that we can control both the background and the perturbation equations allowing us to construct the higher derivative extension of mimetic dark matter and the mimetic nonsingular bouncing scenarios. The latter can be thought as a new higher derivative effective action for the loop quantum cosmology scenario in which the equations of motion coincide with those suggested by loop quantum cosmology. We investigate a possible connection between the mimetic cosmology and the Randall-Sundrum cosmology.