  Massive fields during inflation provide an interesting opportunity to test
new physics at very high energy scales. Meanwhile in fundamental realizations,
the inflationary field space typically has a curved geometry, which may leave
detectable imprints in primordial observables. In this paper we study an
extension of quasi-single field inflation where the inflaton and the massive
field belong to a curved field manifold. Because of the nontrivial field space
curvature, the massive field here can get significant mass corrections of order
the Hubble scale, thus the quasi-single field predictions on primordial
non-Gaussianity are affected. We derive the same result in an equivalent
approach by using the background effective field theory of inflation, where a
dimension-6 operator is identified to play an important role and its cutoff
scale is associated with the curvature scale of the field space. In addition,
due to the slow-roll evolution of the inflaton, this type of mass correction
has intrinsic time-dependence. Consequently, the running mass modifies the
scaling behaviour in the squeezed limit of the scalar bispectrum, while the
resulting running index measures the curvature of the internal field space.
Therefore the minimal setup of a massive field within curved field space during
inflation may naturally lead to new observational signatures of the field space
geometry.
