A General Model for Dark Energy Crossing the Phantom Divide

Abstract: Within the framework of spatially covariant theories, we propose a general model for dark energy (DE) in which the cosmological background and perturbations are independently controlled by different sets of coefficients, and the equation of state of DE is directly determined by two free functions of time from the Lagrangian. These properties allow to realize arbitrary background evolutions while avoiding ghost and gradient instabilities in linear perturbations. They also enable a more direct analysis of phantom crossing without having to first solve the background equations of motion. In this model, the sound speed of the scalar mode is scale-dependent and approaches infinity at large scale, so that the field becomes non-dynamical in the infrared (IR) limit. Even though this usually indicates a strong coupling issue, we speculate that this is avoided because the scalar degree of freedom becomes frozen not only at linear order but also at any higher order in IR limit. Given this characteristic large scales behavior, we dub the model \emph{Freezing Gravity}. On smaller scales, the scalar mode propagates with a finite speed of sound. The theory has a cut-off in energy, signaled by the pole in the speed of sound, when the effective Planck mass exceeds Planck mass.