Vacuum Coherence and the Nanohertz Gravitational-Wave Background: A Bayesian Analysis within the Elastic Universe Theory (TUE)

This study presents a Bayesian analysis of the nanohertz gravitational-wave background (GWB) detected by the NANOGrav and IPTA collaborations between 2023 and 2025, interpreted within the framework of the Elastic Universe Theory (TUE). The model treats the vacuum as a quantized elastic medium, whose coherent deformations generate both gravitational waves and cosmological acceleration. A stochastic Landau formulation with colored noise at 2 and 16 nHz and cosmological feedback (ηH) reproduces the observed amplitude and spectral slope of the GWB. The Bayesian fit yields r* = 0.10 ± 0.01, τ = (5 ± 2)×10⁹ yr, and η = 1.5 ± 0.7, fully consistent with PTA data. These results suggest that approximately 20% of the dark-energy density may originate from elastic vacuum coherence, linking quantum gravity, dark energy, and gravitational-wave cosmology