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 spacetime
fields and the large-scale dynamics of the universe emerge from the projection and relaxation
of this underlying spectral field. In this work we combine the theoretical foundations with
the complete numerical implementation. Spectral tension Ts =
R
K
|∇kΦ(k)|
2 d
nk replaces
the cosmological constant as the driver of cosmic acceleration. Cosmic expansion is shown
to be the geometric manifestation of irreversible spectral decoherence. The observed Hubble
tension arises naturally as a direct consequence of the continuous loss of global spectral
coherence 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 current
coherence fraction c0 = 0.4406 fixed solely by the measured Hubble tension (Hlocal
0 = 73.50
vs HCMB
0 = 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 tension
via 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 once
systematic uncertainties are accounted for.
The DFF framework eliminates the need for a dark matter particle and a separate dark
energy field, deriving both from the single principle of spectral coherence relaxation. It
maintains the same effective parameter count as ΛCDM while providing first-principles
explanations for the major cosmological tensions.

Improved explanations from version 1