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 f NL 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 f NL . 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 f NL , 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 f NL =−10 +270 −260 at the 2σ level (Bayesian) and f NL =−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 f NL 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 f NL =−5 ± 85 and f NL =−5 ± 175 at the 1σ and 2σ level respectively using the frequentist approach.