Natural FLRW metrics on the Lie group of nonzero quaternions

TL;DR

This paper demonstrates that the Lie group of invertible quaternions naturally admits a family of closed FLRW metrics, linking quaternion algebra structures with cosmological metric models.

Contribution

It introduces a novel connection between quaternion Lie groups and FLRW cosmological metrics, expanding the mathematical framework of cosmology.

Findings

Lie group of invertible quaternions admits natural closed FLRW metrics

Establishes a mathematical link between quaternion algebra and cosmological models

Provides a new geometric perspective on FLRW metrics

Abstract

It is shown that the Lie group of invertible elements of the quaternion algebra carries a family of natural closed Friedmann-Lemaitre-Robertson-Walker metrics.