# Towards a viable effective field theory of mimetic gravity

## TL;DR

This paper analyzes mimetic gravity theories with curvature-scalar couplings, showing that under homogeneous scalar field assumptions, these models are viable effective field theories with three degrees of freedom, resolving previous instability issues.

## Contribution

It derives degeneracy conditions for mimetic gravity with higher derivatives and clarifies the degrees of freedom in homogeneous versus non-homogeneous backgrounds.

## Key findings

- Homogeneous scalar field configurations lead to three degrees of freedom.
- Hamiltonian analysis reveals four or more degrees of freedom in general.
- Singular Dirac matrix reduces degrees of freedom to three in homogeneous cases.

## Abstract

We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the FLRW background for this kind of models. Restricting to homogeneous scalar field configurations in the action, we derive degeneracy conditions to obtain an effective field theory with three degrees of freedom. However, performing the Hamiltonian analysis for a generic scalar field we show that there are in general four or more degrees of freedom. The discrepancy is resolved because, for a homogeneous scalar field profile, $\partial_i\varphi\approx 0$, the Dirac matrix becomes singular, resulting in further constraints, which reduces the number of degrees of freedom to three. Similarly, in linear perturbation theory the additional scalar degree of freedom can only be seen by considering a non-homogeneous background profile of the scalar field. Therefore, restricting to homogeneous scalar fields these kinds of models provide viable explicitly Lorentz violating effective field theories of mimetic gravity.