The Tension of Space as Dark Energy: A No Geometric Sequestering Theorem for Minimal Sequesters

TL;DR

This work addresses the cosmological constant problem by modeling space as an elastic three-brane with a uniform volume tension $T_s$ and embedding it in a minimal four-form sequestering framework that neutralizes constant matter vacuum energy. The authors show, via a no-geometric-neutralization argument, that constant shifts in the matter sector cancel in the combination $T^{(m)}_{\mu\nu} - \Lambda g_{\mu\nu}$, while the purely geometric term proportional to $T_s$ does not couple to the global constraints and remains in the local field equations. Gravitational EFT analysis demonstrates that $T_s$ runs with the renormalization scale $\mu$, producing an effective cosmological term $T_s(\mu)$ that sources $G_{\mu\nu} = -T_s(\mu) \, g_{\mu\nu} + \cdots$, which can be identified with dark energy at IR scales. The framework thus preserves sequestering of arbitrary matter vacuum energy while predicting a residual geometric contribution that can match observations, with potential extensions to dynamical dark energy via elastic-space rheology such as bulk viscosity. The results offer a covariant EFT perspective on the origin of dark energy and a concrete mechanism for its small but nonzero value within a minimal sequestering setup.

Abstract

We model space as an elastic membrane and identify its uniform tension $T_s$ with the vacuum energy density of space. The central result is a no geometric sequestering theorem. In any minimal matter vacuum sequester framework where a global constraint cancels constant contributions from the matter sector by adjusting a global variable, a purely geometric unit operator remains intact. Concretely a volume term of the form $S_s = - T_s \int \sqrt{-g} \, d^4 x$ does not couple to the global variable that enforces the matter cancellation and it survives unchanged in the local field equations. We establish this result within a covariant effective field theory using the background field method. The analysis shows that the coefficient $T_s$ is renormalized by graviton loops and in general by mixed matter-graviton loops and therefore runs with the renormalization scale $μ$. The running defines an effective cosmological term $T_s(μ)$ that is present even after the matter vacuum energy has been neutralized by the sequester constraint. In particular we find that $T_s(μ)$ sources $G_{μν} = - T_s(μ) \, g_{μν} + \cdots$. The tension term $T_s(μ)$ can then be understood as residual dark energy in the minimal sequestering framework.