Listening to Celestial Algebras

TL;DR

This paper explores how normed division algebras like quaternions and octonions can model elementary particles and cosmological symmetries, potentially leading to observable effects in gravitational wave data.

Contribution

It introduces novel applications of division algebras to cosmology and particle physics, linking algebraic structures to observable phenomena.

Findings

Division algebras enable new realizations of the cosmological principle

Potential observational signatures in gravitational wave astronomy

Interplay between quaternionic and octonionic symmetry groups

Abstract

In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting non-trivial realisations of the cosmological principle with an interplay between the symmetry groups of the quaternions and octonions. We also argue how these realisations give rise to potentially observational signatures in gravitational waves astronomy.