WMAP 9-Year vs Pattern Field Theory

Independent baseline cross-check of PFT using WMAP’s final 9-year release (maps, TT/TE/EE spectra) alongside Planck 2018 (PR3) comparisons.

Summary

  • Goal: Cross-check PFT against WMAP 9-Year CMB measurements (temperature & polarization).
  • Why WMAP? Provides an independent experiment and pipeline from Planck, useful for robustness checks.
  • Approach: Reproduce TT/TE/EE spectra with official masks; compare characteristic scales and anisotropy features with PFT predictions; inspect hemispherical asymmetry ranges (ℓ ~ 50–250).

Data & Methods

Datasets:

  1. WMAP 9-Year temperature & polarization maps + likelihoods (official release).
  2. Standard masks and beam window functions as provided in the 9-year package.
  3. (Reference) Planck 2018 PR3 SMICA maps and TT/TE/EE likelihoods for qualitative cross-checks.

Processing outline:

  • Apply WMAP masks; compute pseudo-Cℓ, deconvolve beams/window functions.
  • Generate TT/TE/EE spectra over 30 ≤ ℓ ≤ 1000 (extend as S/N allows).
  • Evaluate large-scale hemispherical asymmetry windows (e.g., ℓ ∈ [50, 250]).
  • Compare salient scales and smoothness with Planck 2018 (qualitative sanity check).

Note: This page is a methods+results container. Plots will be embedded below as they are generated.

PFT Predictions to Test (CMB)

  • Fractal scale-invariance signature at ~10−5 levels in the anisotropy field (containment, not “size”).
  • Directional asymmetries (~μK scale) consistent with field-local time emergence.
  • Substrate-coherence smoothness consistent with Pi-Matrix closure across multipoles.

For the full list of PFT predictions and definitions, see the canonical JSON compendium and related articles.

Open PFT Compendium (JSON)

Results (Starter)

Status: This starter page is live and wired for plots. As soon as you upload figures into /articles/cmb/wmap-9-year/figures/ they will render below.

TT Power Spectrum (WMAP 9-Year)

TODO: Export plot as figures/wmap9_tt.png.

WMAP 9-Year TT Power Spectrum

TE / EE Spectra

TODO: Export plots as figures/wmap9_te.png and figures/wmap9_ee.png.

WMAP 9-Year TE WMAP 9-Year EE

Hemispherical Asymmetry (ℓ 50–250)

TODO: Export map/plot as figures/wmap9_hemi_asym.png.

WMAP 9-Year Hemispherical Asymmetry

PFT vs WMAP: Initial Comparison Notes

  • Global morphology: Expect broad agreement with Planck on TT peaks/dips; use this as a sanity check against PFT’s Pi-Matrix smoothness expectations.
  • Fractal signature: Run your scale-invariance measure on WMAP maps; confirm ~10−5 level structure if present.
  • Asymmetry band (ℓ ~ 50–250): Check for directional bias consistent with PFT’s time-emergence claim.

Once figures are added, summarize numeric comparisons here (e.g., peak locations, residuals vs. baseline, any μK asymmetry metrics).

References

  • WMAP 9-Year: final maps, likelihoods, and results (official release).
  • Planck 2018 (PR3): legacy TT/TE/EE likelihoods and SMICA maps (reference).
  • Pattern Field Theory (PFT): site articles and canonical JSON compendium.