Turning a Newtonian analogy for FLRW cosmology into a relativistic problem

TL;DR

This paper explores how a Newtonian analogy for expanding cosmological models can be extended into a relativistic framework, revealing new insights and analogies in general relativity.

Contribution

It introduces methods to implement the Newtonian FLRW analogy within general relativity and uncovers related new cosmological analogies.

Findings

Quasilocal energy remains Newtonian, unaffected by the magnetic Weyl tensor.

Symmetries in Einstein-Friedmann equations have counterparts in Newtonian systems.

New relativistic cosmological analogies are derived from the Newtonian framework.

Abstract

A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always `Newtonian' in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system.