GaussianCMBHypothesis - crowlogic/arb4j GitHub Wiki

Based on the 2001 paper by Gupta and Heavens and subsequent experimental results, here is the status of the Gaussian CMB hypothesis:

Status: CONFIRMED (to extremely high precision)

The Gaussian hypothesis has not been ruled out—in fact, it has been robustly confirmed by subsequent CMB observations. The 2001 paper you cite was a theoretical methods paper that developed tools to test Gaussianity, anticipating future data from missions like MAP (WMAP) and Planck.

Key Findings from That 2001 Paper:

  • Developed an exact method to compute the correlation function of peaks in Gaussian random fields on a sphere (generalizing earlier flat-sky calculations)
  • Showed that peak statistics could be more sensitive than the bispectrum for detecting certain non-Gaussian signatures
  • Demonstrated that cosmic string models produced detectable non-Gaussian signals in their peak correlation function that would differ from Gaussian predictions

What Subsequent Experiments Found:

WMAP (2001-2010) and especially Planck (2009-2013) provided definitive tests:

  1. Gaussianity holds spectacularly well: The CMB temperature fluctuations follow Gaussian statistics to within measurement precision (better than 1 part in 10,000)
  2. Non-Gaussianity parameters: Constraints on primordial non-Gaussianity (f_NL) are consistent with zero to high precision (|f_NL| < 10 for most shapes)
  3. Anomalies exist but are marginal: Some "anomalies" (e.g., hemispherical asymmetry, cold spot) have been identified but are generally considered not statistically significant enough to reject Gaussianity given the large number of possible tests
  4. Defect models largely ruled out: Topological defect models (cosmic strings, textures) cannot produce the observed near-perfect Gaussianity and have been relegated to sub-dominant roles at best

Current Understanding:

The Gaussian nature of CMB fluctuations is now considered strong evidence for inflationary cosmology and is built into the standard ΛCDM model. The methods developed in your 2001 paper (peak statistics) turned out to be useful for foreground analysis rather than for detecting primordial non-Gaussianity, because the CMB itself proved to be so remarkably Gaussian.

Bottom line: The hypothesis was essentially proven correct by observations, not ruled out.