Spacetime algebraic skeleton

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.Comment: 13 page

Primeval symmetries

A detailed examination of the Killing equations in Robertson-Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product U = (a^2)(dH/dt) of the squared scale parameter by the time-derivative of the Hubble function encapsulates the relationship between the two cases: the symmetry is maximal when U is a constant, and reduces to the six-parameter symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the fields physical interpretation is not clear in these coordinates, comparison is made with the Killing fields in static coordinates, whose interpretation is made clearer by their direct relationship to the Poincare group generators via Wigner-Inonu contractions.Comment: 16 pages, 2 tables; published versio

The Equivalence Principle Revisited

A precise formulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity, but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: "An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed". This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.Comment: RevTeX, 18 pages, no figures, to appear in Foundations of Physic

de Sitter relativity: a natural scenario for an evolving Lambda

The dispersion relation of de Sitter special relativity is obtained in a simple and compact form, which is formally similar to the dispersion relation of ordinary special relativity. It is manifestly invariant under change of scale of mass, energy and momentum, and can thus be applied at any energy scale. When applied to the universe as a whole, the de Sitter special relativity is found to provide a natural scenario for the existence of an evolving cosmological term, and agrees in particular with the present-day observed value. It is furthermore consistent with a conformal cyclic view of the universe, in which the transition between two consecutive eras occurs through a conformal invariant spacetime.Comment: V1: 11 pages. V2: Presentation changes, new discussion added, 13 page