Inflation with Gauss-Bonnet coupling

Abstract: We consider inflationary models with the inflaton coupled to the Gauss-Bonnet term assuming a special relation $\delta_1=2\lambda\epsilon_1$ between the two slow-roll parameters $\delta_1$ and $\epsilon_1$. For the slow-roll inflation, the assumed relation leads to the reciprocal relation between the Gauss-Bonnet coupling function $\xi(\phi)$ and the potential $V(\phi)$, and it leads to the relation $r=16(1-\lambda)\epsilon_1$ that reduces the tensor-to-scalar ratio $r$ by a factor of $1-\lambda$. For the constant-roll inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor-to-scalar ratio to the first order of $\epsilon_1$ by using the method of Bessel function approximation. The tensor-to-scalar ratio is reduced by a factor of $1-\lambda+\lambda\tilde \eta$. Comparing the derived $n_s$-$r$ with the observations, we obtain the constraints on the model parameters $\tilde\eta$ and $\lambda$.