lines in the Figure give the numerical exact evolution, while dashed lines the analytic slow-roll approximation. The solid and dashed lines are almost superimposed to each other, signaling the great accuracy of the slow roll approximation.

![ Inflationary evolution of $Q$ (left panel) and of $\epsilon$ (right panel) as a function of the number of e-folds, for two different values of $\gamma_{60}$ (the value $\gamma_{\rm in}$ at $60$ e-folds before the end of inflation). Solid lines in the Figure give the numerical exact evolution, while dashed lines the analytic slow-roll approximation. The solid and dashed lines are almost superimposed to each other, signaling the great accuracy of the slow roll approximation. []{data-label="fig:Q-eps-bck"}](Q_SR "fig:"){width="45.00000%"} ![ Inflationary evolution of $Q$ (left panel) and of $\epsilon$ (right panel) as a function of the number of e-folds, for two different values of $\gamma_{60}$ (the value $\gamma_{\rm in}$ at $60$ e-folds before the end of inflation). Solid lines in the Figure give the numerical exact evolution, while dashed lines the analytic slow-roll approximation. The solid and dashed lines are almost superimposed to each other, signaling the great accuracy of the slow roll approximation. []{data-label="fig:Q-eps-bck"}](epsilon-SR "fig:"){width="45.00000%"}

Linear perturbations {#sec:linpert}
====================

In this Section, we study at 