Constraints on fNL and gNL from the analysis of the N-pdf of the CMB large-scale anisotropies

In this paper, we extend a previous work where we presented a method based on the N-point probability density function (pdf) to study the Gaussianity of the cosmic microwave background (CMB). We explore a local non-linear perturbative model up to third order as a general characterization of the CMB anisotropies. We focus our analysis in large-scale anisotropies (theta > 1 degrees). At these angular scales (the Sachs-Wolfe regime), the non-Gaussian description proposed in this work defaults (under certain conditions) to an approximated local form of the weak non-linear coupling inflationary model. In particular, the quadratic and cubic terms are governed by the non-linear coupling parameters f(NL) and g(NL), respectively. The extension proposed in this paper allows us to directly constrain these non-linear parameters. Applying the proposed methodology to Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data, we obtain -5.6 x 105 < g(NL) < 6.4 x 105, at 95 per cent confidence level. This result is in agreement with previous findings obtained for equivalent non-Gaussian models and with different non-Gaussian estimators, although this is the first direct constraint on g(NL) from CMB data. A model selection test is performed, indicating that a Gaussian model (i.e. f(NL) equivalent to 0 and g(NL) equivalent to 0) is preferred to the non-Gaussian scenario. When comparing different non-Gaussian models, we observe that a pure f(NL) model (i.e. g(NL) equivalent to 0) is the most favoured case and that a pure g(NL) model (i.e. f(NL) equivalent to 0) is more likely than a general non-Gaussian scenario (i.e. f(NL) not equal 0 and g(NL) not equal 0). Finally, we have analysed the WMAP data in two independent hemispheres, in particular the ones defined by the dipolar pattern found by Hoftuft et al. We show that, whereas the g(NL) value is compatible between both hemispheres, it is not the case for f(NL) (with a p-value of approximate to 0.04). However, if, as suggested by Hoftuft et al., anisotropy of the data is assumed, the distance between the likelihood distributions for each hemisphere is larger than expected from Gaussian and anisotropic simulations, not only for f(NL) but also for g(NL) (with a p-value of approximate to 0.001 in the case of this latter parameter). This result is extra evidence for the CMB asymmetries previously reported in WMAP data.