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 $\xi (\varphi )$ and the potential $V(\varphi )$, 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 $\lambda$.

26 pages, 7 figures, major changes, conclusion remains unchanged, PRD in press