  The calculation of scalar gravitational and matter perturbations during
multiple-field inflation valid to first order in slow roll is discussed. These
fields may be the coordinates of a non-trivial field manifold and hence have
non-minimal kinetic terms. A basis for these perturbations determined by the
background dynamics is introduced, and the slow-roll functions are generalized
to the multiple-field case. Solutions for a perturbation mode in its three
different behavioural regimes are combined, leading to an analytic expression
for the correlator of the gravitational potential. Multiple-field effects
caused by the coupling to the field perturbation perpendicular to the field
velocity can even contribute at leading order. This is illustrated numerically
with an example of a quadratic potential. (The material here is based on
previous work by the authors presented in hep-ph/0107272.)
