Structure formation and effective theories

Abstract

Structure formation is one of the pillars of modern cosmology. The main tool for the study of the large-scale structures (LSS) of the Universe is the two-point function, which takes the form of the correlation function in real (configuration) space, or the power spectrum in Fourier space.One of the most fundamental tests of our cosmological models comes from comparing the theoretically computed two-point functions with observations from galaxy surveys, and precision tests based on those physical observables are becoming increasingly important to test the standard cosmological model.However there is a basic simplification on the way we compute these 2-point functions, in that we usually assume that all points belong to the same $t=$constant hypersurface, when in reality our observations are always carried out on our past light cone.This distinction is relevant because we are now at a time when the observational tests using 2-point functions demand high precision for the theoretical calculations.The good news is that there are a few ways that we can compute these 2-point functions, in ways that allow us to keep track of the time in a systematic way. In particular, standard perturbation theory (SPT) and the Effective Field Theory of Large-Scale Structure (EFTofLSS) allow us to compute these 2-point functions using points at different time slices.In this Scientific Initiation project the student will be introduced to some advanced topics in cosmology and structure formation, in particular cosmological perturbation theory. In an intermediate stage, we will start workin on effective theories and the EFTofLSS, taking care that we keep track of the time evolution at higher orders in the perturbations.Towards the end of the project we plan to study a potential new physical observable: the commutator of the two-point function in two different $t=$constant hypersurfaces, namely: $C(\vec{k},\vec{k'};\eta_1,\eta_2) = \langle \delta(\vec{k},\eta_1)\delta(\vec{k'},\eta_2) - \delta(\vec{k},\eta_2)\delta(\vec{k'},\eta_1) \rangle \; $.