Thermodynamic Interpretation of Finite-Domain Vacuum Energy and the Cosmological Constant

This paper is part of a research program proposing that the cosmological constant arises not from total vacuum energy but from the finite-domain residual to which gravity actually couples.

This paper develops the seventh and final component of a research program examining the thermodynamic interpretation of the finite-domain vacuum energy residual that acts as the cosmological constant.

The cosmological constant problem is conventionally framed as a discrepancy between the enormous vacuum energy density suggested by quantum field theory and the small value inferred from cosmological observations. In a series of preceding papers, we argued that this discrepancy arises from comparing two categorically different quantities: the total zero-point energy computed over an infinite domain and the finite residual vacuum energy that survives within a finite causal domain. Paper 1 established that the vacuum ground state is physically real, maximally symmetric, and energetically full. Paper 2 showed that quantum field theory computes state-energy using an infinite domain, then the result is incorrectly applied to a finite, growing universe — a category error. Within the corrected framework, gravitational consistency and holographic entropy bounds lead to a residual vacuum energy density of the form ρ_Λ = αℏc/(ℓ_p²L²), where L characterizes the size of the finite causal domain and α is a dimensionless coefficient determined by the microscopic structure of the vacuum fluctuations. The present paper develops the thermodynamic interpretation of this finite-domain residual. Using the Gibbons–Hawking temperature and Bekenstein–Hawking entropy of the cosmological horizon, we show that the same 1/L² scaling emerges as the natural equilibrium energy scale of a horizon-bounded system. The thermodynamic estimate differs from the microscopic spectral result by a factor N/(6π), where N counts the independent quantum field degrees of freedom, providing a quantitative bridge between the macroscopic thermodynamic description and the microscopic fluctuation spectrum. We further examine the evolution of the gravitational consistency bound along the particle horizon and find that, for the coefficient α determined in earlier papers, the bound approaches saturation near the present cosmological epoch, constituting a non-trivial internal consistency check of the framework. The results suggest that the cosmological constant may be interpreted as the equilibrium finite-domain vacuum energy compatible with the finite entropy of the cosmological horizon.

Series Context

This paper forms the seventh and final component of the Finite-Domain Vacuum Energy research program addressing the cosmological constant problem. Papers 1–2 establish the conceptual framework by distinguishing vacuum state-energy from the gravitationally operative residual energy within a finite causal domain. Papers 3–4 derive the gravitational consistency scaling ρΛ ∝ ħc/(ℓp²L²) and show that the resulting cosmological self-consistency condition reproduces the observed cosmic composition. Papers 5–6 connect the numerical coefficient of this scaling to the particle content and spectral structure of the quantum vacuum, showing that α = N/(16π²) arises from channel counting of the vacuum fluctuation spectrum.

The present paper provides the thermodynamic interpretation of this framework. Using the Gibbons–Hawking temperature and Bekenstein–Hawking entropy of the cosmological horizon, it shows that the same 1/L² scaling emerges as the natural equilibrium energy scale of a horizon-bounded system. The thermodynamic estimate differs from the microscopic spectral result by a factor N/(6π), providing a quantitative bridge between the macroscopic thermodynamic description and the microscopic fluctuation spectrum. The analysis also examines the evolution of the gravitational admissibility bound through cosmic history and shows that, for the coefficient α determined in the earlier papers, the bound approaches saturation near the present cosmological epoch, providing an internal consistency relation within the framework.