Multifractal and Phase-Coherence Signatures in the WMAP 9-Year W-Band Temperature Field: Evidence for Non-Gaussian Structure Beyond Gaussian ΛCDM

We present a joint multifractal and phase-coherence analysis of the WMAP 9-year W-band CMB temperature anisotropy map, using a framework based on the τ(q) multifractal spectrum and the phase-coherence envelope Rℓ. A suite of Gaussian Monte Carlo simulations matched to the empirical Cℓ distribution provides percentile confidence intervals for both statistics. The observed WMAP data exhibit significant deviations from Gaussian expectations at three scales: (i) a low-ℓ phase-coherence excess (ℓ ≲ 40), (ii) a structured acoustic-peak-scale coherence depression and recovery (100 ≲ ℓ ≲ 400), and (iii) a sustained high-ℓ excess (ℓ ≳ 600). These features correlate with departures in the τ(q) multifractal spectrum, particularly for q > 0, where the observed τ(q) lies persistently above the Monte Carlo median envelope. The combined statistical evidence suggests that the WMAP temperature field contains non-Gaussian structure that cannot be reproduced by phase-randomized or Gaussian ΛCDM surrogates with identical angular power spectra. The results demonstrate the sensitivity of multifractal and phase-coherence diagnostics to subtle higher-order correlations and motivate re-examination of the assumptions underlying Gaussian initial conditions and mode independence.