A mechanism for formation of Bose-Einstein condensation in cosmology

We introduce a toy model of scalar particles with a trilinear scalar coupling in cosmology. The trilinear coupling $\phi^2\chi$ causes production of non-relativistic $\phi$ particles through the process $\chi\chi\,\rightarrow\,\phi\phi$ where, initially, only relativistic $\chi$ particles are present. We consider the initial times of $\chi\chi\,\rightarrow\,\phi\phi$ and observe that the curved space effects promote formation of Bose-Einstein condensate of $\phi$ particles.