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Scalar field cosmologies with a generalized harmonic potential areinvestigated in flat and negatively curvedFriedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interactionbetween the scalar field and matter is considered. Asymptotic methods andaveraging theory are used to obtain relevant information about the solutionspace. In this approach, the Hubble parameter plays the role of atime-dependent perturbation parameter which controls the magnitude of the errorbetween full-system and time-averaged solutions as it decreases. Our approachis used to show that full and time-averaged systems have the same asymptoticbehavior. Numerical simulations are presented as evidence of such behavior.Moreover, the asymptotic behavior of the solutions is independent of thecoupling function.

A Perturbative Analysis of Interacting Scalar Field Cosmologies