The universe is not a lie, but actually an Hopf, algebra

Abstract

In this paper, I would like to show how the Deformed Special Relativity family of models — developed to approach spacetime quantization — can actually be applied to the description of classical cosmology. I use the bicrossproduct basis of κ-Poincaré algebra to describe photon propagation in de Sitter classical General Relativity. I show the Hopf algebraic aspects of de Sitter model, and give an explicit physical interpretation of κ-Poincaré Hopf algebraic features in spacetime. Such an approach allows to unravel some not-yet-known General Relativistic relations of de Sitter cosmology, and reinterpret many features of Quantum Gravity phenomenology as classical properties of maximally symmetric spacetime models. In the last section of the paper, I give a first example on how to apply this mathematical framework to more realistic (nonmaximally symmetric) spacetime models such as ΛCDM and matter-dominated universe.