The tension of space as dark energy: dynamics and phenomenology

Abstract

We develop a phenomenological model in which the observed late-time dark-energy sector is interpreted as an effective residual tension of space. Motivated by recent observational hints that the dark-energy equation of state may exhibit mild low-redshift evolution, we begin with an intrinsic membrane description of spacetime and show that a uniform space tension contributes to the gravitational field equations with precisely the tensor structure of vacuum energy. We then consider a Dirac--Born--Infeld completion, which naturally introduces a hidden Abelian gauge sector. A late-time hidden transition, \(U(1)_h \, \to \, \mathbb{Z}_n\), can reorganize hidden magnetic energy into a coarse-grained flux-tube reservoir. If this reservoir exchanges energy with the dynamical part of the space-tension sector, the effective dark-energy density becomes time dependent and acquires a nontrivial equation of state. At the background level, the model gives a simple proof-of-concept realization of running dark energy and admits a transient crossing of the phantom divide. A restricted numerical scan shows that the best representative solution corresponds to a string-like hidden flux reservoir, with an effective low-redshift evolution that projects approximately to $(w_0^{\mathrm{mod}},w_a^{\mathrm{mod}})\simeq (-0.915,-0.457)$ in the Chevallier--Polarski--Linder plane. This does not exactly reproduce the compressed observational benchmark, but it generates a phenomenologically relevant departure from \(\Lambda\)CDM and illustrates how a late hidden-sector defect population can induce mild running of the residual vacuum-like tension of space. The construction is therefore best viewed as a physically transparent proof of concept rather than a complete theory of dark energy.

Comments: 41 pages, 4 figures, 3 tables. Published in Indian Journal of Physics. This is the author-prepared version