Energy and momentum of the Friedmann and more general universes

TL;DR

This paper challenges previous coordinate-dependent results by demonstrating, through coordinate-independent methods, that the energy and momentum of Friedmann and similar universes are not necessarily zero, emphasizing the importance of proper calculation techniques.

Contribution

It introduces coordinate-independent expressions for energy and momentum, showing that these universes can have non-zero energy and momentum contrary to earlier coordinate-dependent conclusions.

Findings

Coordinate-independent methods reveal non-zero energy and momentum.

Previous zero-energy results depend on coordinate choices.

Friedmann universes are not necessarily energy-less.

Abstract

Recently some authors concluded that the energy and momentum of the Fiedman universes, flat and closed, are equal to zero locally and globally (flat universes) or only globally (closed universes). The similar conclusion was also done for more general only homogeneous universes (Kasner and Bianchi type I). Such conclusions originated from coordinate dependent calculations performed only in comoving Cartesian coordinates by using the so-called {\it energy-momentum complexes}. But it is known that the energy-momentum complexes can be reasonably use only in precisely defined asymptotically flat spacetimes (at null or at spatial infinity) to calculate global energy and momentum. In this paper we show, by using new coordinate independent expressions on energy and momentum that the Friedman and more general universes {\it needn't be energetic nonentity}.