  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.
