  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.
