Cosmic inflation in a landscape of heavy fields

Heavy isocurvature fields may have a strong influence on the low energy dynamics of curvature perturbations during inflation, as long as the inflationary trajectory becomes non-geodesic in the multi-field target space (the landscape). If fields orthogonal to the inflationary trajectory are sufficiently heavy, one expects a reliable effective field theory describing the low energy dynamics of curvature perturbations, with self-interactions determined by the shape of the inflationary trajectory. Previous work analyzing the role of heavy-fields during inflation have mostly focused in the effects on curvature perturbations due to a single heavy-field. In this article we extend the results of these works by studying models of inflation in which curvature perturbations interact with two heavy-fields. We show that the second heavy-field (orthogonal to both tangent and normal directions of the inflationary trajectory) may significantly affect the evolution of curvature modes. We compute the effective field theory for the low energy curvature perturbations obtained by integrating out the two heavy-fields and show that the presence of the second heavy-field implies the existence of additional self-interactions not accounted for in the single heavy-field case. We conclude that future observations will be able to constrain the number of heavy fields interacting with curvature perturbations.