Spacetime algebraic skeleton

TL;DR

This paper reveals that the cosmological constant Lambda has an algebraic origin as an eigenvalue of a Lorentz group Casimir invariant, suggesting a fundamental algebraic 'skeleton' underlying spacetime geometry.

Contribution

It introduces the concept of a spacetime algebraic skeleton based on Lorentz group invariants, linking Lambda to algebraic structures in tangent spaces of all spacetimes.

Findings

Lambda is an eigenvalue of a Lorentz Casimir invariant.

A fundamental algebraic structure underlies the geometry of all physical spacetimes.

Tetrad fields connect the algebraic skeleton to specific spacetime geometries.

Abstract

The cosmological constant Lambda, which has seemingly dominated the primaeval Universe evolution and to which recent data attribute a significant present-time value, is shown to have an algebraic content: it is essentially an eigenvalue of a Casimir invariant of the Lorentz group which acts on every tangent space. This is found in the context of de Sitter spacetimes but, as every spacetime is a 4-manifold with Minkowski tangent spaces, the result suggests the existence of a "skeleton" algebraic structure underlying the geometry of general physical spacetimes. Different spacetimes come from the "fleshening" of that structure by different tetrad fields. Tetrad fields, which provide the interface between spacetime proper and its tangent spaces, exhibit to the most the fundamental role of the Lorentz group in Riemannian spacetimes, a role which is obscured in the more usual metric formalism.