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We consider the long time behavior of solutions to scalar field modelsappearing in the theory of cosmological inflation (oscillons) and cold darkmatter, in presence or absence of the cosmological constant. These models arenot included in standard mathematical literature due to their unusualnonlinearities, which model different features to classical ones. Here we provethat these models fit in the theory of dispersive decay by computing newvirials adapted to their setting. Several important examples, candidates tomodel both effects are studied in detail.

A proof of slow-roll local decay of inflaton fields in cosmology and axion fields in cold dark matter models