On local decay of inflaton and axion fields

We consider the long time behavior of solutions to scalar field models appearing in the theory of cosmological inflation, oscillons and cold dark matter, in presence or absence of the cosmological constant. These models are not included in standard mathematical literature due to their unusual nonlinearities, which model different features with respect to classical fields. Here we prove that these models fit in the theory of dispersive decay by computing new virials adapted to their setting. Several examples, candidates to model both effects are studied in detail.