Abstract
The problem is solved of describing scale factors of a homogeneous isotropic spaces-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. Explicit expressions for dependence of time from the large-scale factor are presented in the form of Abelian integrals in these cases. The exact solution for a scalar field with Gauss-Bonnet type coupling with curvature is received and it is shown that the corresponding nonconformal additions can dominate at the particles creation by gravitational field.
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