Inhomogeneous vacuum energy

TL;DR

This paper explores inhomogeneous vacuum energy as a model for dark energy, providing a covariant framework for its perturbations and showing how it can be decomposed into interacting vacuum and matter components with simple perturbation equations.

Contribution

It introduces a covariant description of inhomogeneous vacuum energy and derives gauge-invariant perturbation equations, enabling a unified treatment of dark energy models.

Findings

Inhomogeneous vacuum energy can be consistently described with a covariant approach.

Dark energy cosmologies can be decomposed into interacting vacuum and matter components.

Perturbations obey simple first-order equations.

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.