A Predictive Dark Energy Model from Group Field Theory

We present a predictive dark‑energy scenario rooted in the Group Field Theory (GFT) condensate cosmology framework. Matter particles are localised coherent excitations — private spacetimes — that perturb the global FLRW metric. The homogeneous condensate gives a negligible vacuum energy, while the incoherent virtual foam of Planck‑scale 4‑simplices provides dark energy. Its collective effect is modelled by a minimally coupled scalar field \( \bar\phi \) with a natural initial amplitude ~ M_P and an exponential potential \( V(\bar\phi)=V_0 e^{-\lambda_{\rm DE}\bar\phi/MP} \), adopted as a well‑motivated effective ansatz. The minimal coupling is supported by an explicit projection calculation showing that the foam collective mode is orthogonal to the original condensate modulus. Working in the physical frame where the Planck mass is constant and matter is minimally coupled, we avoid fifth‑force issues. Using the covariant entropy bound on the apparent horizon, the energy scale of the foam is shown to be parametrically of order M_P²H₀², naturally explaining the meV scale. The slope λ_DE is estimated semi‑analytically from the scaling dimension of the leading foam operator, giving λ_DE ~ 0.65, and further constrained by cosmological data. After fixing the potential normalisation V₀ to the observed dark‑energy density, the dynamics is controlled by this single parameter. A numerical integration of the thawing scalar yields an equation of state with w₀ ≃ -0.86, w_a < 0, and a suppression of linear matter growth relative to ΛCDM, in broad agreement with current observations. A Fisher forecast indicates that Stage‑IV surveys (DESI, Euclid) will decisively distinguish this model from a cosmological constant. In contrast to recent GFT‑based phantom dark‑energy models, this model predicts a thawing evolution with a clear observational signature. Detailed derivations and all numerical checks are provided in the accompanying Supplementary Material.