Mass hierarchies and non-decoupling in multi-scalar field dynamics

In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the `heavy' directions arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the low energy effective theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the trajectory can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to the trajectory if the trajectory turns sharply enough. These effects could be important during inflation, which could lead to detectable effects in upcoming observations.