— Title:
Generalized Slow-Roll approach for Horndeski inflation —  

Abstract:
In the canonical realization of inflation, the primordial power spectra are usually computed in terms of a standard hierarchy of the slow-roll parameters, related to the inflaton potential, which are required to be small and constant. However, there exist well-motivated models whose inflationary potential exhibits features that break this hierarchy. The Generalized Slow-Roll (GSR) approach provides an efficient tool to overcome the problems of the standard slow-roll procedure. Furthermore, models with non-canonical terms in the Lagrangian arise naturally in other contexts, as in particle physics, and satisfy observations as well. Horndeski theory (and its extensions) is the most general scalar-tensor theory with second-order equations of motion. It covers canonical inflation as well as several non-canonical models proposed in the literature. In this talk I will present the recent and ongoing developments made on GSR and, in particular, on its applications to Horndeski inflation. —