The Dynamical Fourier Field Resolution of the Hubble Tension: Coherence Decay, Residual Spectral Force, and the Elimination of Dark Matter

We present a comprehensive formulation of the Dynamical Fourier Field (DFF) frame-work as a unified resolution to the Hubble tension. The fundamental entity is a complex-valued spectral field Φ : K → C defined over a spectral manifold K. All physical spacetimefields and the large-scale dynamics of the universe emerge from the projection and relaxationof this underlying spectral field. In this work we combine the theoretical foundations withthe complete numerical implementation. Spectral tension Ts =RK|∇kΦ(k)|2 dnk replacesthe cosmological constant as the driver of cosmic acceleration. Cosmic expansion is shownto be the geometric manifestation of irreversible spectral decoherence. The observed Hubbletension arises naturally as a direct consequence of the continuous loss of global spectralcoherence between the early (CMB) and late (local) universe. Using a power-law coher-ence decay Cglobal(z) = Cglobal(0)(1 + z)αC with parameters αC = 0.035240 and currentcoherence fraction c0 = 0.4406 fixed solely by the measured Hubble tension (Hlocal0 = 73.50vs HCMB0 = 67.24 km s−1Mpc−1), the model reproduces the CMB acoustic peaks exactly,predicts a phantom spectral tension equation of state w0 ≈ −1.0093, resolves the S8 tensionvia the Residual Spectral Force (RSF) free-streaming suppression (σ8 = 0.763, S8 = 0.777)and yields a universe age of 12.71–12.85 Gyr fully consistent with stellar chronometry oncesystematic uncertainties are accounted for.The DFF framework eliminates the need for a dark matter particle and a separate darkenergy field, deriving both from the single principle of spectral coherence relaxation. Itmaintains the same effective parameter count as ΛCDM while providing first-principlesexplanations for the major cosmological tensions. Improved explanations from version 1