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The covariant gauge invariant perturbation theory of scalar cosmologicalperturbations is developed for a general Scalar-TensorFriedmann-Lemaitre-Robertson-Walker cosmology in a vacuum. The perturbationequations are then solved exactly in the long wavelength limit for a specificcoupling, potential and background. Differences with the minimally coupled caseare briefly discussed.Comment: 19 pages, 3 figures, accepted for publication on PR

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case