de Sitter Space Decay and Cosmological Constant Relaxation in Unimodular Gravity with Charged Membranes

Abstract

General covariant unimodular gravity frameworks, based on the Henneaux-Teitelboim formulation, are, in disguise, precisely $4$-form field theories corrected with higher dimension operators. In the presence of charged tensional membranes, any de Sitter space in all such theories is unstable and decays. If the fluxes sourced by membranes are mutually incommensurate, de Sitter geometries comprise a very refined discretuum of states. Whenever the $4$-form sector is dominated by terms linear in flux the almost-Minkowski space is the unique long-time attractor. As a result, a tiny cosmological constant is natural in all such frameworks, without appealing to anthropic reasoning.