The formation of the large structures of the Universe results from gravitational instability, which pushes dark matter to collapse, forming a network (called the cosmic web) of dense voids, sheets, filaments, and knots. Each element of the cosmic web is based on the local dimensionality of the gravitational collapse, which is equal to the number of positive eigenvalues of the tidal field. Thus, a point is part of a knot, filament or wall if it has respectively 3, 2 or 1 positive eigenvalue, if it has no positive eigenvalue, it is part of a void.

Using 2000 different ΛCDM model of the Quijote suite of N-Body simulations, we studied the properties of non-linearity and non-Gaussianity of the cosmic web by distinguishing each element and according to the cosmological model. Several observables have been calculated, for each category individually, namely: i) Mass and volume filling fractions, ii) the probability distribution function P (δ) and its first 4 moments iii) The power spectrum P (k). We also calculated the cross-correlations between the 4 categories, as well as the cross-correlations between each category and the matter field.

Our results show that each category has its own non-linear and non-Gaussian characteristics for a given cosmological model, and that the geometric and dynamical properties of each category depend differently on the cosmological parameters, in particular on Ω_m and σ₈. We were also able to constrain the n_s and Ω_b parameters by isolating respectively the walls and filaments properties.
We finally show that, instead of relying only on the matter field, the use of the cosmic web information allows a finer understanding of the origin of the nonlinear and non-Gaussian properties of the gravitational instability according to cosmological models, and much better inference of all cosmological parameters.