Octonionic Gravi-electromagnetism and Dark Matter

TL;DR

This paper explores how octonions can unify electromagnetic and gravitational theories, providing new formulations for dark matter and analyzing differences between hot and cold dark matter in an octonionic framework.

Contribution

It introduces a novel octonionic approach to unify electromagnetic and gravitational interactions and models dark matter within this algebraic structure.

Findings

Derived field equations for unified gravi-electromagnetic interactions.

Reconstructed dark matter equations using split octonions.

Highlighted differences between hot and cold dark matter in structure formation.

Abstract

An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic unified gauge formulation for SU(2) ?X U(1) electroweak theory and SU(3) X? SU(2) ?X U(1) grand unified theory. De- scribing the octonion eight dimensional space as the combination of two quaternionic spaces (namely associated with the electromagnetic interaction (EM-space) and linear gravitational interaction (G-space)), we have reexamined the unified picture of EM-G space in terms of oc- tonionic split formulation in consistent manner. Consequently, we have obtained the various field equations for unified gravi-electromagnetic interactions. Furthermore, we have recon- structed the field equations of hot and cold dark matter in terms of split octonions. It is shown that the difference between the octonion cold dark matter (OCDM) and the octonion hot dark matter (OHDM) is significant in the formulating of structure of these two, because the velocities of octonion hot dark matter cause it to wipe out structure on small scales.