# Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations

## TL;DR

This paper develops an effective scalar-tensor theory to create a stable model of mimetic dark matter that avoids gradient and ghost instabilities, addressing issues in previous models.

## Contribution

It introduces a new instability-free extension of mimetic dark matter using the ADM formalism within scalar-tensor theories.

## Key findings

- Constructed a model free from ghost and gradient instabilities.
- Demonstrated that mimetic F(R) theory has Ostrogradsky instability.
- Provided a framework for stable imperfect dark matter models.

## Abstract

We study the stability of a recently proposed model of scalar-field matter called mimetic dark matter or imperfect dark matter. It has been known that mimetic matter with higher derivative terms suffers from gradient instabilities in scalar perturbations. To seek for an instability-free extension of imperfect dark matter, we develop an effective theory of cosmological perturbations subject to the constraint on the scalar field's kinetic term. This is done by using the unifying framework of general scalar-tensor theories based on the ADM formalism. We demonstrate that it is indeed possible to construct a model of imperfect dark matter which is free from ghost and gradient instabilities. As a side remark, we also show that mimetic $F({\cal R})$ theory is plagued with the Ostrogradsky instability.