Gauss–Bonnet inflation with a constant rate of roll

In the model of the inflaton nonminimal coupling to the Gauss–Bonnet term, we discuss the constant-roll inflation with constant $$\epsilon _1$$ ϵ 1 , constant $$\epsilon _2$$ ϵ 2 and constant $$\eta _H$$ η H , respectively, with the additional assumption that $$\delta _1$$ δ 1 is a constant. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index $$n_{\mathcal {R}}$$ n R and the tensor to scalar ratio r to the first order of $$\epsilon _1$$ ϵ 1 . By using the Planck 2018 observations constraint on $$n_{\mathcal {R}}$$ n R and r, we obtain some feasible parameter space and show the result on the $$n_{\mathcal {R}}-r$$ n R - r region. The scalar potential is also reconstructed in some special cases.