On creation of scalar particles with Gauss-Bonnet type coupling to curvature in Friedmann cosmological models

Calculations are presented for creation of massive and massless scalar particles coupled to Gauss-Bonnet type curvature in Friedmann cosmological models. It has been shown that, for fields of mass~$m$, the effect of the coupling parameter $\zeta$ with the Gauss-Bonnet invariant is insignificant if $\zeta m^2 \ll 1 $. In all cases under consideration, the created particle number is compatible by order of magnitude with the number of causally disconnected space-time regions by the Compton time, corresponding $1/m$ or $\sqrt{\zeta}$.