Space, Matter and Interactions in a Quantum Early Universe. Part I : Kac-Moody and Borcherds Algebras

TL;DR

This paper proposes a quantum model for the early universe's expansion, utilizing algebraic extensions of Kac-Moody and Borcherds algebras to describe particle interactions and creation.

Contribution

It introduces a novel quantum framework based on extended Kac-Moody and Borcherds algebras for modeling early universe dynamics and quantum gravity.

Findings

Algebraic extensions drive space and matter expansion.

New generalized algebraic structures meet quantum gravity requirements.

Framework links algebraic structures with cosmological evolution.

Abstract

We introduce a quantum model for the Universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac-Moody Lie algebra $\mathbf{e_9}$. We investigate Kac-Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.