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

We test the consistency of estimates of the non-linear coupling constant fNL using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of fNL. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, 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. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on fNL, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate fNL=-10+270-260 at the 2σ level (Bayesian) and fNL=-10+310-270 (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of fNL and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain fNL=-5 +/- 85 and fNL=-5 +/- 175 at the 1σ and 2σ level respectively using the frequentist approach.