In writing a covariant effective action for single-field inflation, one is allowed to add a Gauss-Bonnet and axion-type curvature couplings. These couplings represent modifications of gravity, and are the unique higher-curvature terms that lead to second order equations of motion in four dimensions. In this paper we study the observational consequences of such couplings for models with large non-Gaussianities. Our focus is on the Gauss-Bonnet term. In particular, we study an effective action where the scalar Lagrangian is a general function of the inflaton and its first derivative. We show that, for large non-Gaussianities, one can write $f_{\mathrm{NL}}$ in terms of only three parameters. The shape of $f_{\mathrm{NL}}$ is also studied, and we find that it is very similar to that of $k$-inflation. We show that the Gauss-Bonnet term enhances the production of gravitational waves, and allows a smaller speed of sound for scalar perturbations. This, in turn, can lead to larger non-Gaussianities which can be constrained by observations. Using current Wilkinson microwave anisotropy probe limits on $f_{\mathrm{NL}}$ and the tensor/scalar ratio, we put constraints on all parameters. As an example, we show that for Dirac-Born-Infeld inflation, the Gauss-Bonnet coupling leads to an interesting observational window with both large $f_{\mathrm{NL}}$ and a large amplitude of gravitational waves. Finally, we show that the Gauss-Bonnet coupling admits a de Sitter phase with a relativistic dispersion relation for scalar perturbations.

• Received 17 June 2008

DOI:https://doi.org/10.1103/PhysRevD.79.043520