Two-field mimetic gravity revisited and Hamiltonian analysis

TL;DR

This paper revisits the two-field mimetic gravity model, analyzing its degrees of freedom and stability at both linear and non-linear levels, revealing additional scalar modes and potential ghost instabilities.

Contribution

The study provides a comprehensive Hamiltonian analysis of the two-field mimetic gravity model, clarifying the number of degrees of freedom and stability issues, including cases with opposite sign kinetic terms.

Findings

Two scalar degrees of freedom identified beyond tensor modes.

Hamiltonian analysis confirms the linear perturbation results.

Opposite sign kinetic terms lead to ghost instabilities.

Abstract

We revisit the two-field mimetic gravity model with shift symmetries recently proposed in the literature, especially the problems of degrees of freedom and stabilities. We first study the model at the linear cosmological perturbation level by quadratic Lagrangian and Hamiltonian formulations. We show that there are actually two (instead of one) scalar degrees of freedom in this model in addition to two tensor modes. We then push on the study to the full non-linear level in terms of the Hamiltonian analysis, and confirm our result from the linear perturbation theory. We also consider the case where the kinetic terms of the two mimetic scalar fields have opposite signs in the constraint equation. We point out that in this case the model always suffers from the ghost instability problem.