Energy of cosmological spacetimes and perturbations: a quasilocal approach * *Sections 2 and 3 of this paper are an expanded version of the essay ‘quasilocal conservation laws in cosmology: a first look’ [], awarded honorable mention in the gravity research foundation 2020 awards for essays on gravitation.

Abstract

Quasilocal definitions of stress–energy–momentum—that is, in the form of boundary densities (rather than local volume densities)—have proven generally very useful in formulating and applying conservation laws in general relativity. In this paper, we present a detailed application of such definitions to cosmology, specifically using the Brown–York quasilocal stress–energy–momentum tensor for matter and gravity combined. We compute this tensor, focusing on the energy and its associated conservation law, for FLRW spacetimes with no pertubrations and with scalar cosmological perturbations. For unperturbed FLRW spacetimes, we emphasize the importance of the vacuum energy (for both flat and curved space), which is almost universally underappreciated (and usually ‘subtracted’), and discuss the quasilocal interpretation of the cosmological constant. For the perturbed FLRW spacetime, we show how our results recover or relate to the more typical effective local treatment of energy in cosmology, with a view toward better studying the issues of the cosmological constant and of cosmological back-reactions.