2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/41117The 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.)11 pages, 2 figures. Talk given at COSMO-01 Workshop, Rovaniemi, Finland, August 30 - September 4, 2001High Energy Physics - Phenomenologytext