Primordial non-Gaussianity: local curvature method and statistical significance of constraints on f_NL from WMAP data

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Abstract
We test the consistency of estimates of the non-linear coupling constant f_NL using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs significantly from the method used to obtain f_NL in previous works. Nevertheless, using spherical wavelets we find results in very good agreement with (Mukherjee and Wang 2004), showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. Using this method, we estimate f_NL=30 +/- 210 at the 2 sigma level. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f_NL, and discuss the relation between the two approaches. The two procedures produce markedly different outcomes, proving that a careful analysis on their different interpretations is needed.

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