Inhomogeneous vacuum energy

Vacuum energy remains the simplest model of dark energy which could drive the accelerated expansion of the Universe without necessarily introducing any new degrees of freedom. Inhomogeneous vacuum energy is necessarily interacting in general relativity. Although the 4-velocity of vacuum energy is undefined, an interacting vacuum has an energy transfer and the vacuum energy defines a particular foliation of spacetime. In particular we will discuss cosmological solutions where the background vacuum energy is spatially homogeneous. It is possible to give a consistent description of vacuum dynamics and in particular the relativistic equations of motion for spatially inhomogeneous perturbations given a covariant prescription for the vacuum energy, or equivalently the energy transfer 4-vector, and we construct gauge-invariant vacuum perturbations. We show that any dark energy cosmology can be decomposed into an interacting vacuum+matter cosmology whose inhomogeneous perturbations obey simple first-order equations. (paper)