Quasi-single field inflation in the non-perturbative regime

In quasi-single field inflation there are massive fields that interact with the inflaton field. If these other fields are not much heavier than the Hubble constant during inflation ($H$) these interactions can lead to important consequences for the cosmological energy density perturbations. The simplest model of this type has a real scalar inflaton field that interacts with another real scalar $S$ (with mass $m$). In this model there is a mixing term of the form $\mu \dot{\pi }S$, where $\pi$ is the Goldstone fluctuation that is associated with the breaking of time translation invariance by the time evolution of the inflaton field during the inflationary era. In this paper we study this model in the region $(\mu /H{)}^2+(m/H{)}^2>9/4$ and $m/H\sim O\left(1\right)$ or less. For a large part of the parameter space in this region standard perturbative methods are not applicable. Using numerical and analytic methods we study how large $\mu /H$ has to be for the large $\mu /H$ effective field theory approach to be applicable.