  In this paper we analyze scalar gravitational perturbations on a
Robertson-Walker background in the presence of multiple scalar fields that take
values on a (geometrically non-trivial) field manifold during slow-roll
inflation. For this purpose modified and generalized slow-roll functions are
introduced and their properties examined. These functions make it possible to
estimate to what extent the gravitational potential decouples from the scalar
field perturbations. The correlation function of the gravitational potential is
calculated in an arbitrary state. We argue that using the vacuum state seems a
reasonable assumption for those perturbations that can be observed in the CMBR.
Various aspects are illustrated by examples with multiple scalar fields that
take values on flat and curved manifolds.
