Energy of cosmological spacetimes and perturbations: a quasilocal approach *

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