Note on the Conservation of Quasi-Local Energy in an Expanding Universe

TL;DR

This paper investigates the concept of energy conservation in an expanding universe using the Brown-York quasi-local energy definition, addressing fundamental questions in general relativity.

Contribution

It applies the Brown-York quasi-local energy framework to analyze energy conservation in expanding or collapsing universes, clarifying a complex theoretical issue.

Findings

Energy conservation depends on the quasi-local energy definition.

In an expanding universe, total energy is not globally conserved but can be understood locally.

The Brown-York approach offers insights into energy behavior in dynamic spacetimes.

Abstract

Whether energy is conserved in a universe which keeps expanding is an intriguing question. It is tempting to argue that the total energy within the universe would have to increase as the universe expands. Upon more detailed inspection the question is a lot harder to settle since defining what is meant by energy or even what is meant by energy being conserved is a difficult problem in general relativity. Using the definition of quasi-local energy provided by Brown and York we try to answer the question in which sense the total energy in an expanding (or collapsing) universe is conserved.