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This research focuses on scalar field cosmologies with a generalized harmonicpotential. Our attention is centred on the anisotropic LRS Bianchi I and IIImetrics, Bianchi V metrics, and their isotropic limits. We provide acomprehensive overview of the first two metrics classes and offer new findingsfor Bianchi V metrics. We show that the Hubble parameter is a time-dependentperturbation parameter that controls the magnitude of the error betweenfull-system and time-averaged solutions as it decreases, such that thosecomplete and time-averaged systems have the same asymptotic behaviour.Therefore, oscillations entering the system can be controlled and smoothed out,which simplifies the problem at hand.

Averaging generalized scalar field cosmologies IV: locally rotationally symmetric Bianchi V model