Multi-field Cuscuton cosmology

In this paper, we first introduce a multi-field setup of Cuscuton gravity in a curved field space manifold. Then, we show that this model allows for a regular bouncing cosmology and it does not lead to ghosts or other instabilities at the level of perturbations. More precisely, by decomposing the scalar fields perturbations into the tangential and normal components with respect to the background field space trajectory, the entropy mode perpendicular to the background trajectory is healthy which directly depends on the signature of the field-space metric, whereas the adiabatic perturbation tangential to the background trajectory is frozen. In analogy with the standard Cuscuton theory equipped with an extra dynamical scalar field, the adiabatic field does not have its own dynamics, but it modifies the dynamics of other dynamical fields like entropy mode in our scenario. Finally, we perform a Hamiltonian analysis of our model in order to count the degrees of freedom propagated by dynamical fields.