This paper concludes our semi-analytic study of preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. Using the covariant framework of paper I in this series, we extend the rigid-spacetime results of paper II by considering both the expansion of the universe during preheating, as well as the effect of the coupled metric perturbations on particle production. The adiabatic and isocurvature perturbations are governed by different effective masses that scale differently with the nonminimal couplings and evolve differently in time. The effective mass for the adiabatic modes is dominated by contributions from the coupled metric perturbations immediately after inflation. The metric perturbations contribute an oscillating tachyonic term that enhances an early period of significant particle production for the adiabatic modes, which ceases on a time-scale governed by the nonminimal couplings $xi_I$. The effective mass of the isocurvature perturbations, on the other hand, is dominated by contributions from the fields potential and from the curvature of the field-space manifold (in the Einstein frame), the balance between which shifts on a time-scale governed by $xi_I$. As in papers I and II, we identify distinct behavior depending on whether the nonminimal couplings are small ($xi_I lesssim {cal O} (1)$), intermediate ($xi_I sim {cal O} (1 - 10)$), or large ($xi_I geq 100$).
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