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 four-velocity of vacuum energy is undefined,
an interacting vacuum has an energy transfer and the vacuum energy defines a
particular foliation of spacetime with spatially homogeneous vacuum energy in
cosmological solutions. It is possible to give a consistent description of
vacuum dynamics and in particular the relativistic equations of motion for
inhomogeneous perturbations given a covariant prescription for the vacuum
energy, or equivalently the energy transfer four-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.
