Classical and quantum Vainshtein: applications to inflation and modified gravity

Abstract: Effective Field Theory (EFT) tools offer an excitingly simple dictionary by which one constructs predictions of a given theory, while giving insights into its regime of validity. In cosmology they have become increasingly popular to describe models of the early and late universe, even though these are completely distinct periods in the history of our universe. I will discuss a specific class of models where the interactions are of kinetic (or derivative) nature, rather than purely potential. They all have in common the so-called Vainshtein or kinetic mechanism, which I will argue is crucial not only classically, but also quantum-mechanically. On the early universe front I will apply the EFT formulation to these theories to describe their limitations and as a case study I will elaborate on DBI inflation for concreteness. For modified gravity theories that screen a fifth-force I will discuss k-essence models as well as galileons. I will present some preliminary developments in future directions these theories can take.