Preheating with non-minimally coupled scalar fields in higher-curvature inflation models

In higher-curvature inflation models ($R+\alpha_n R^n$), we study a parametric preheating of a scalar field $\chi$ coupled non-minimally to a spacetime curvature $R$ ($\xi R \chi^2$). In the case of $R^2$-inflation model, efficient preheating becomes possible for rather small values of $\xi$, i.e. $|\xi|< several. Although the maximal fluctuation$\sqrt{< \chi^2 >}_{max} \approx 2 \times10^{17}$GeV for$\xi \approx -4$is almost the same as the chaotic inflation model with a non-minimally coupled$\chi$field, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for$R^4$model and find that the maximal fluctuation is$\sqrt{< \chi^2 >}_{max} \approx 8 \times 10^{16}$GeV for$\xi \approx -35$.