Numerical and EFT realization of a single domain effective Cosmic Broth cosmology

Modern cosmology rests on the empirical success of ΛCDM, yet its dominant components—dark energy and dark matter—remain phenomenological placeholders. The cosmological constant is inserted rather than derived; the origin of late-time acceleration remains conceptually unresolved. In this work, we advance the Cosmic Broth program from a structural hypothesis into a fully testable cosmological framework. We propose that cosmic acceleration emerges from the relaxation dynamics of an effective vacuum substrate, described by a scalar order parameter Φ\PhiΦ minimally coupled to General Relativity but conformally coupled to matter. Rather than modifying gravity itself, we allow the vacuum sector to respond dynamically to matter density, producing environment-dependent behavior without altering the Einstein–Hilbert structure. The theory contains ΛCDM as a limiting case: when the relaxation field freezes, the model reduces to a cosmological constant. However, when the substrate evolves slowly, it generates small but measurable deviations in both expansion history and structure growth. The key physical ingredient is a density-dependent effective potential. Matter sources the relaxation field, shifting its instantaneous minimum. In high-density environments the field is driven differently than in low-density cosmological regions, producing a natural screening-like mechanism. The vacuum becomes responsive rather than rigid. At the background level, the model reproduces the standard expansion history with small controlled departures parametrized by a coupling strength β\betaβ. These deviations remain consistent with current constraints while permitting non-trivial late-time dynamics. The most distinctive signatures arise in structure formation. The relaxation field mediates a finite-range fifth force whose strength depends on scale. On sufficiently large scales, standard gravity is recovered. On smaller scales, clustering is enhanced by a factor proportional to β2\beta^2β2. This leads to: A shift in the growth index γ\gammaγ, Scale-dependent modifications of the growth rate, Enhanced nonlinear clustering at intermediate scales, No gravitational slip at linear order. The absence of anisotropic stress distinguishes the framework from many modified gravity models: lensing and dynamical mass remain consistent, while clustering strength changes. To ensure observational viability, we embed the model into the Effective Field Theory of Dark Energy (EFT-of-DE) formalism. In Jordan frame language, the theory maps to a restricted Horndeski subclass with luminal tensor speed and a specific structural relation between EFT functions: αB=−αM.\alpha_B = - \alpha_M.αB=−αM. This relation provides a sharp falsifiable signature. If future surveys favor EFT regions incompatible with this constraint, the model is ruled out. We further outline nonlinear N-body implementations, showing how the substrate-mediated interaction modifies the matter power spectrum and halo statistics. The theory predicts enhanced clustering at k≳0.2 h/Mpck \gtrsim 0.2\,h/\mathrm{Mpc}k≳0.2h/Mpc, correlated shifts in S8S_8S8, and mild scale-dependent redshift-space distortions—effects testable with upcoming surveys. Importantly, the framework does not introduce exotic kinetic structures, superluminal propagation, or higher-derivative operators. Stability conditions are satisfied in the canonical regime, and ΛCDM is smoothly recovered for vanishing coupling. This work transforms the Cosmic Broth idea from interpretative language into a concrete dark-sector theory compatible with modern cosmological pipelines. It demonstrates that an emergent vacuum relaxation picture can be made mathematically precise, observationally constrained, and phenomenologically distinct from both ΛCDM and generic quintessence. Whether the vacuum is a constant or a medium remains an empirical question. This model makes that question testable.