The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes

TL;DR

This paper investigates how the magnetic part of the Weyl tensor affects the large-scale expansion in discrete mass cosmological models, showing its influence grows with time and number of masses, reaching about 1%.

Contribution

It introduces the magnetic part of the Weyl tensor into the evolution equations of discrete universe models and analyzes its increasing impact over time.

Findings

Magnetic Weyl tensor influence increases with the number of masses.

The magnetic part can contribute up to ~1% to the universe's scale.

Impact grows over cosmological time, affecting expansion dynamics.

Abstract

We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of ~1%, before the Taylor series approximation starts to break down.