Quasilocal Energy in FRW Cosmology

TL;DR

This paper calculates the quasilocal energy in FRW cosmology, demonstrating correct small-sphere behavior, differences from classical results, and comparing formulations to identify the most accurate approach.

Contribution

It provides a novel calculation of quasilocal energy in non-stationary FRW models and compares different formulations to determine which aligns with classical limits.

Findings

Brown and York formulation does not match classical limit

Epp's formulation correctly reproduces classical energy

Higher order corrections are identified in the energy calculations

Abstract

This paper presents a calculation of the quasilocal energy of a generic FRW model of the universe. The results have the correct behavior in the small-sphere limit and vanish for the empty Milne universe. Higher order corrections are found when comparing these results to classical calculations of cosmological energy. This case is different from others in the literature chiefly in that it involves a non-stationary spacetime. This fact can be used to differentiate between the various formulations of quasilocal energy. In particular, the formulation due to Brown and York is compared to that of Epp. Only one of these is seen to have the correct classical limit.