Global existence of the self-interacting scalar field in the de Sitter universe

We present some sufficient conditions for the global in time existence of solutions of the semilinear Klein-Gordon equation of the self-interacting scalar field with complex mass. The coefficients of the equation depend on spatial variables as well, that makes results applicable, in particular, to the spacetime with the time slices being Riemannian manifolds. The least lifespan estimate is given for the class of equations including the Higgs boson equation, which according to physics has a finite lifetime.