Despite the wealth of P lanck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependencies. Aiming at detecting the NGs of the CMB temperature anisotropy δT , while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function P (δT ), related to v 0 , the first Minkowski Functional (MF), and the two other MFs, v 1 and v 2 . From their analytical Gaussian predictions we build the discrepancy functions ∆ k (k=P,0,1,2 ) which are applied to an ensemble of 10 5 CMB realization maps of the ΛCDM model and to the P lanck CMB maps. In our analysis we use general Hermite expansions of the ∆ k up to the 12 th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the 2 nd order expansions of Matsubara to arbitrary order in the standard deviation σ 0 for P (δT ) and v 0 , where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the ΛCDM map sample and the P lanck data. We confirm the weak level of non-Gaussianity (1-2)σ of the foreground corrected masked P lanck 2015 maps.

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric assumes comoving spatial rigidity of metrical properties. The curvature term in comoving coordinates is environmentindependent and cannot evolve. In the standard model, structure formation is interpreted accordingly: structures average out on the chosen metrical background, which remains rigid in comoving coordinates despite nonlinear structure growth. The latter claim needs to be tested, since it is a hypothesis that is not derived using general relativity. We introduce a test of the comoving rigidity assumption by measuring the two-point auto-correlation function on comoving scales-assuming FLRW comoving spatial rigidity-in order to detect shifts in the baryon acoustic oscillation (BAO) peak location for Luminous Red Galaxy (LRG) pairs of the Sloan Digital Sky Survey Data Release 7. In tangential directions, subsets of pairs overlapping with superclusters or voids show the BAO peak. The tangential BAO peak location for overlap with Nadathur & Hotchkiss superclusters is 4.3 ± 1.6h −1 Mpc less than that for LRG pairs unselected for supercluster overlap, and 6.6 ± 2.8h −1 Mpc less than that of the complementary pairs. Liivamägi et al. superclusters give corresponding differences of 3.7 ± 2.9h −1 Mpc and 6.3 ± 2.6h −1 Mpc, respectively. We have found moderately significant evidence (Kolmogorov-Smirnov tests suggest very significant evidence) that the BAO peak location for supercluster-overlapping pairs is compressed by about 6% compared to that of the complementary sample, providing a potential challenge to FLRW models and a benchmark for predictions from models based on an averaging approach that leaves the spatial metric a priori unspecified.