A First-Order Gauge Approach to de Sitter General Relativity

Abstract

We propose a first-order gauge formulation of de Sitter relativity in which the pseudo-radius l(x) is promoted to a spacetime field, locally breaking SO(4,1) to SO(3,1). Here, l(x) is a geometric compensator and dl(x) the associated order parameter. This modifies the Strong Equivalence Principle: the local vacuum follows the matter distribution instead of remaining fixed, while the propagating degrees of freedom of General Relativity are unchanged. At fixed l(x), the action is SO(3,1)-gauge invariant, but varying l(x) destroys covariance under the full translational sector of SO(4,1). Through the Inonu-Wigner contraction, abstract generators become explicit spacetime transformations, yielding nonlinear Killing vectors in both the macroscopic l tends to infinity and microscopic l tends to 0 limits. The generalized Noether theorem gives a unified energy-momentum current coupling the standard tensor to the proper conformal matter current. It vanishes identically without matter, causing the asymptotic extinction of local vacuum energy and the decay of the background to Minkowski spacetime. Independent variations yield the coupled de Sitter field equations, and we algebraically prove their equivalence to the tensorial splitting on the coordinate manifold. Gauge Bianchi identities further show that Lambda(x) is an intrinsic source of spacetime torsion, consistently identifying it with the local order parameter of the symmetry breaking. The cosmological constant problem is therefore recast, not numerically solved: deriving the decay of Lambda(x) from early-universe densities to its observed value remains future work.