Global existence of the scalar field in de Sitter spacetime

In this article we prove the global existence of the small data solutions of the Cauchy problem for the semilinear Klein–Gordon equation in the de Sitter spacetime. Unlike the same problem in the Minkowski spacetime, we have no restriction on the order of nonlinearity and structure of the nonlinear term, provided that a physical mass of the field is outside of some bounded interval.