Separating fast and slow scales in perturbative dynamical systems

Abstract: In this talk, we will review some of the conundrums of standard big bang cosmology and a few proposals designed to circumvent them. To do so, we study the quantum origin of perturbations in a perfect (or imperfect) fluid and show some useful techniques to calculate their corresponding two-point correlators. Our objective is to improve the accuracy and efficiency of the existing methods to evaluate primordial power spectra of scalar and tensor fluctuations, and therefore provide solid observational constraints. Our approach is to rewrite all the relevant equations of motion in terms of slowly varying quantities, which is important to consider the contribution from high-frequency modes to the spectrum without affecting computational performance. We do not require additional approximations to reproduce all the features in the power spectrum for each specific early universe model.