Spacetime algebraic skeleton

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.