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Constraining Primordial Non-Gaussianities from the WMAP2 2-1 Cumulant Correlator Power Spectrum

Gang Chen, Istvan Szapudi

TL;DR

This study constrains primordial non-Gaussianity by measuring the 2-1 cumulant correlator power spectrum $C_l^{21}$, a degenerate bispectrum, from WMAP data using the SpICE method to account for sky geometry. The authors relate $C_l^{21}$ to the full bispectrum and generate theory with a modified CAMB at $f_{NL}=1$, enabling prediction up to $l\approx 2000$; they estimate covariances with 200 Gaussian simulations and address the huge covariance matrix via a novel SVD-based compression. Random Matrix Theory is employed to show the covariance is dominated by noise, justifying a diagonal $\chi^2$ approach and enabling robust constraints on $f_{NL}$. The resulting constraint, $f_{NL}=22\pm 52$ (1$\sigma$), is consistent with Gaussian primordial fluctuations and prior analyses, demonstrating that the 2-1 cumulant correlator is a viable, geometry-aware probe of non-Gaussianity in current CMB data and a scalable framework for future surveys.

Abstract

We measure the 2-1 cumulant correlator power spectrum $C^{21}_l$, a degenerate bispectrum, from the second data release of the Wilkinson Microwave Anisotropy Probe (WMAP). Our high resolution measurements with SpICE span a large configuration space ($\simeq 168\times999$) corresponding to the possible cross-correlations of the maps recorded by the different differencing assemblies. We present a novel method to recover the eigenmodes of the correspondingly large Monte Carlo covariance matrix. We examine its eigenvalue spectrum and use random matrix theory to show that the off diagonal terms are dominated by noise. We minimize the $χ^2$ to obtain constraints for the non-linear coupling parameter $f_{NL} = 22 \pm 52 (1σ)$.

Constraining Primordial Non-Gaussianities from the WMAP2 2-1 Cumulant Correlator Power Spectrum

TL;DR

This study constrains primordial non-Gaussianity by measuring the 2-1 cumulant correlator power spectrum , a degenerate bispectrum, from WMAP data using the SpICE method to account for sky geometry. The authors relate to the full bispectrum and generate theory with a modified CAMB at , enabling prediction up to ; they estimate covariances with 200 Gaussian simulations and address the huge covariance matrix via a novel SVD-based compression. Random Matrix Theory is employed to show the covariance is dominated by noise, justifying a diagonal approach and enabling robust constraints on . The resulting constraint, (1), is consistent with Gaussian primordial fluctuations and prior analyses, demonstrating that the 2-1 cumulant correlator is a viable, geometry-aware probe of non-Gaussianity in current CMB data and a scalable framework for future surveys.

Abstract

We measure the 2-1 cumulant correlator power spectrum , a degenerate bispectrum, from the second data release of the Wilkinson Microwave Anisotropy Probe (WMAP). Our high resolution measurements with SpICE span a large configuration space () corresponding to the possible cross-correlations of the maps recorded by the different differencing assemblies. We present a novel method to recover the eigenmodes of the correspondingly large Monte Carlo covariance matrix. We examine its eigenvalue spectrum and use random matrix theory to show that the off diagonal terms are dominated by noise. We minimize the to obtain constraints for the non-linear coupling parameter .

Paper Structure

This paper contains 8 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. power spectrum of 2-1 cumulant correlator
  3. Measurements and Predictions
  4. The Covariance Matrix and $\chi^2$ Analysis
  5. The Covariance Matrix
  6. Binning
  7. Random Matrix Theory
  8. Results and Discussion

Figures (2)

  • Figure 1: A typical results of the 2-1 cumulant power spectrum normalized to the triplet $X = (Q1,Q2,V1)$. The lower solid curve is the theoretical prediction for $f_{NL}=-100$; the upper solid line is the standard deviation from 200 simulations; the dotted line corresponds to the absolute values from WMAP2. Inset: the data (without absolute value) and theory on a linear scale renormalized by the standard deviation measured from the simulations.
  • Figure 2: The eigenvalue spectrum for a set of power mapped CMs from 200 WMAP2 simulations and from the 200 random matrix simulations. The original matrix corresponds to $q=1$. To display more detail, we plot unbinned (sorted) eigenvalues of our CM along with those obtained from random matrix simulations. The spectacular agreement indicates that the random matrix assumption is fairly accurate.