Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models

We solve the problem of describing scaling factors of a homogeneous isotropic space–time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. We give explicit expressions in the form of Abelian integrals for the dependence of time on the scaling factor in these cases. We obtain an exact solution for the scalar field coupled to the Gauss–Bonnet-type curvature and show that the corresponding nonconformal contributions can dominate in particle creation by the gravitational field.