dS QNMs and PBHs beyond the Gaussian limit

In this thesis we propose two (non standard) mathematical methods to deal with different aspects of theoretical cosmology. The first problem we face is the computation of Quasinormal Modes (QNMs) of oscillation of a scalar field on a pure de Sitter (dS) background with an S-matrix like approach. In a QFT on de Sitter background, one can study correlators between fields pushed to the future and past horizons of a comoving observer. This is a neat probe of the physics in the observer’s causal diamond (known as the static patch). We use this observable to give a generalization of the quasinormal spectrum in interacting theories, and to connect it to the spectral density that appears in the Källén-Lehmann expansion of dS correlators. We also introduce a finite-temperature effective field theory consisting of free bulk fields coupled to a boundary. In matching it to the low frequency expansion of correla- tors, we find positivity constraints on the EFT parameters following from unitarity. The second problem is the computation of the Primordial Black Holes (PBHs) abundance in a mathematical framework called Peak Theory. The method is independent on the specific inflationary model that one considers and therefore is general. We compute the probability density distribution of maxima for a scalar random field in the presence of local non-gaussianities. The physics outcome of this analysis is the following. If we focus on maxima whose curvature is larger than a certain threshold for gravitational collapse, our calculations illustrate how the fraction of the Universe’s mass in the form of PBHs changes in the presence of local non-gaussianities.