Constraints on f_nl and g_nl from the analysis of the N-pdf of the CMB large scale anisotropies

[Abridged] In this paper 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. At these angular scales, 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, 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 WMAP 5-yr data, we obtain -5.6 x 10^5 < g_nl < 6.4 x 10^5, at 95% CL. This result is in agreement with previous findings obtained for equivalent non-Gaussian models and with different non-Gaussian estimators. A model selection test is performed, indicating that a Gaussian model is preferred to the non-Gaussian scenario. When comparing different non-Gaussian models, we observe that a pure f_nl model is the most favoured case, and that a pure g_nl model is more likely than a general non-Gaussian scenario. Finally, we have analyzed the WMAP data in two independent hemispheres, in particular the ones defined by the dipolar pattern found by Hoftuft et al. 2009. We show that, whereas g_nl is still compatible with zero for both hemispheres, it is not the case for f_nl (with a p-value 0.04). However, if anisotropy of the data is assumed, the distance between the likelihood distributions for each hemisphere is larger than expected from Gaussian and anisotropic simulations, also for g_nl (with a p-value of 0.001 in the case of this parameter). This result is an extra evidence for the CMB asymmetries previously reported in WMAP data.Comment: 15 pages, 9 figures, accepted for publication in MNRAS. Corrections made to match the final versio