A Natural Dark Energy Scale from the Entropy of a Quantum Gravity Foam

The cosmological horizon is not a smooth surface but a mosaic of Planck‑sized quantum pixels – spin‑network punctures. In the early Universe, a far‑from‑equilibrium Coherent–Decoherent Spacetime Transition (CDST) scrambled these pixels, leaving behind a decohered gas of gravitational quanta: a virtual foam. This work shows that the entropy of this foam is the dark energy. Using the boundary‑state counting of Group Field Theory (GFT), we reproduce the Bekenstein–Hawking horizon entropy S = A/(4G). We then define the active foam fraction α_foam, the share of horizon microstates actually occupied by the foam. In the simplest picture, α_foam is simply the fraction of horizon punctures that are decohered and contribute to the cosmic acceleration. Horizon thermodynamics yields the scaling \( \rho_{\mathrm{DE}} \simα_{foam}^{\mathrm{eff}} M_{\mathrm{P}}^{2} H^{2} \), where \( α_{foam}^{\mathrm{eff}} \) absorbs the dynamical temperature correction. The present‑day dark‑energy density parameter is thus \( {\Omega_{\mathrm{DE},0} = \alpha_{\mathrm{foam},0}^{\mathrm{eff}}} \). The observed Ω_DE,0 ≈ 0.69 fixes \( \alpha_{\mathrm{foam},0}^{\mathrm{eff}} \) ≈ 0.69; for the benchmark late‑time background adopted here, the underlying fraction of activated horizon punctures is α_foam,0 ≈ 0.95, a perfectly natural order‑one efficiency. To obtain a consistent expansion history, we embed this holographic scale into a thawing quintessence model with an exponential potential \( V(\bar\phi)=V_{0}\,e^{-\lambda_{\mathrm{DE}}\bar\phi/M_{\mathrm{P}}} \). The slope λ_DE ≃ 0.65 is semi‑analytically estimated from the scaling dimension of the dominant foam operator at the GFT fixed point. Numerical integration yields the equation of state w₀ ≃ -0.86, w_a ≃ -0.15 and a mild suppression of structure growth relative to ΛCDM – predictions that can be stringently constrained by Stage‑IV surveys. A Gaussian entropy formula for α_foam and an illustrative horizon‑cell constraint \( f_{\mathrm{act}}\,\bar{s}\simeq 5.97 \) provide concrete targets for future GFT decoherence calculations. The model also offers a microscopic sequestering argument for the absence of leading fifth forces. The work unifies the microscopic origin of black‑hole entropy with the late‑time cosmic acceleration, turning the dark‑energy puzzle into a quantitatively well‑posed target for future GFT decoherence calculations.