Restoration of the Lorentz symmetry of particle propagator in the ghost condensate model

Abstract

The ghost condensate model has been proposed to protect the vacuum state of the cosmological phantom model yielding the gradient instability regime and the spontaneous Lorentz symmetry breaking in the quantum level with the dispersion relation $\omega^2\sim k^4$. In this paper, we point out that the Lorentz symmetry in the propagator can be restored if the explicit Lorentz symmetry-breaking process is promoted. The particle excitation of the phantom field can propagate through spacetime with the Lorentzian dispersion relation $\omega^2=k^2$ in arbitrary background value. Moreover, the tree-level gradient instability regime can be removed under the characteristic Lorentz violation source of ultraviolet physics.