Multi-field Mimetic Gravity

TL;DR

This paper extends mimetic gravity to a multi-field framework with curved field space, analyzing cosmological implications, perturbation behavior, and ensuring the absence of ghosts through Hamiltonian analysis.

Contribution

It introduces a multi-field mimetic gravity model with curved field space and performs a comprehensive Hamiltonian analysis to confirm its ghost-free nature.

Findings

Mimetic energy density mimics dark matter at the background level

Entropy perturbations propagate with speed of unity, depending on field-space metric signature

System is free from Ostrogradsky ghosts after Hamiltonian analysis

Abstract

In this paper, we extend the mimetic gravity to the multi-field setup with a curved field space manifold. The multi-field mimetic scenario is realized via the singular limit of the conformal transformation between the auxiliary and the physical metrics. We look for the cosmological implications of the setup where it is shown that at the background level the mimetic energy density mimics the roles of dark matter. At the perturbation level, the scalar field perturbations are decomposed into the tangential and normal components with respect to the background field space trajectory. The adiabatic perturbation tangential to the background trajectory is frozen while the entropy mode perpendicular to the background trajectory propagates with the speed of unity. Whether or not the entropy perturbation is healthy directly depends on the signature of the field-space metric. We perform the full non-linear Hamiltonian analysis of the system with the curved field space manifold and calculate the physical degrees of freedom verifying that the system is free from the Ostrogradsky-type ghost.