Analysing the Universe beyond Isotropy, Gaussianity, and Linearity

Plenty of cosmological information can be extracted from 2-point correlation functions of different cosmological fields (i.e., power spectra). However, this tool is insensitive to the presence of anisotropic, inhomogeneous, or non-Gaussian characteristics of the field. In this talk, I will present 3 different approaches that can yield complementary information. First, I will briefly talk about the distribution of matter along the Cosmic Web and, in particular, Cosmic Filaments; I will present an algorithm to detect them and how we can exploit their correlation with other observables. Second, I will talk about higher-order statistics, such as Minkowski Functionals, a tool to describe the geometry and topology of a field; I will talk about how we extended the formalism to CMB polarization and how they can play a role in the analysis of the matter distribution. Lastly, I will talk about how a non-trivial topology of the Universe can break the homogeneity and isotropy of the perturbations and how we can look for these effects in current and future cosmological datasets.