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.
