Inhomogeneous vacuum energy

TL;DR

Addressing how to treat vacuum energy in GR when it is inhomogeneous, the work introduces a covariant formalism with $Q_=-\nabla_\mu V$ that yields vacuum interactions. It shows any homogeneous dark-energy cosmology can be recast as an interacting vacuum+matter system and derives gauge-invariant perturbation equations for the coupled fluids, including a gauge-invariant vacuum perturbation and non-adiabatic pressure terms. The generalized Chaplygin gas is used as a concrete example to show how a late-time vacuum energy can arise as an integration constant in the interacting picture. This framework enables observational constraints on vacuum-energy interactions through perturbations and structure growth, without introducing new dynamical degrees of freedom.

Abstract

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.