Limits on f_NL parameters from WMAP 3yr data

TL;DR

We address primordial non-Gaussianity in the WMAP 3-year CMB data by constraining two theoretically motivated bispectrum shapes: local and equilateral. The authors implement tilt-aware templates, an improved map combination, and updated cosmological parameters to tighten f_NL bounds. No evidence of non-Gaussianity is found; the bounds are -36<f_NL^local<100 and -256<f_NL^equil<332 at 95% CL, with best-fit values near zero. The analysis demonstrates the feasibility of precise bispectrum constraints with current data and outlines expected gains from Planck and polarization measurements.

Abstract

We analyze the 3-year WMAP data and look for a deviation from Gaussianity in the form of a 3-point function that has either of the two theoretically motivated shapes: local and equilateral. There is no evidence of departure from Gaussianity and the analysis gives the presently tightest bounds on the parameters f_ NL^local and f_NL^equil., which define the amplitude of respectively the local and the equilateral non-Gaussianity: -36 < f_NL^local < 100, -256 < f_NL^equil. < 332 at 95% C.L.

Figures (3)

• Figure 1: Effective noise for different combinations of the maps compared with the signal (short-dashed). Optimal signal-to-noise combination (solid); the combination used in the analysis, with $l_{\rm comb} =235$ (dotted); and the noise weighted combination, equivalent to $l_{\rm comb} = 0$ (long-dashed) used in the 1st year analysis Creminelli:2005hu and in the 3yr analysis by the WMAP collaboration Spergel:2006hy.
• Figure 2: Standard deviation for estimators of $f_{\rm NL}^{\rm local}$ as a function of the maximum $l$ used in the analysis. The combination of the maps is done using $l_{\rm comb} = 235$. Lower curve: lower bound deduced from the full sky variance. Lower data points: standard deviation for the trilinear + linear estimator (see details in Creminelli:2005hu). Upper data points: the same for the estimator without linear term used in Spergel:2006hy. The error bars are not independent as the results at different $l$ are all based on the same set of MonteCarlo maps.
• Figure 3: Standard deviation of the estimator of $f_{\rm NL}^{\rm equil.}$ as a function of the maximum $l$ used in the analysis. The combination of the maps is done using $l_{\rm comb} = 235$. Lower curve: lower bound deduced from the full sky variance. Data points: standard deviation for the estimator used in the analysis. The error bars are not independent as the results at different $l$ are all based on the same set of MonteCarlo maps.