Energy of cosmological spacetimes and perturbations: a quasilocal
  approach
  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 towards better studying the
issues of the cosmological constant and of cosmological back-reactions.
