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.

应力-能量-动量的准局部定义——即以边界密度（而不是局部体积密度）的形式——已被证明在广义相对论中制定和应用守恒定律方面通常非常有用。在本文中，我们详细介绍了这些定义在宇宙学中的应用，特别是将布朗-约克准局部应力-能量-动量张量用于物质和重力的组合。我们针对没有扰动和标量宇宙学扰动的 FLRW 时空计算这个张量，重点是能量及其相关的守恒定律。对于未受扰动的 FLRW 时空，我们强调真空能量（对于平坦空间和弯曲空间）的重要性，这几乎普遍被低估（并且通常被“减去”），并讨论了宇宙常数的准局域解释。