Slow-roll Inflation with the Gauss-Bonnet and Chern-Simons Corrections

Abstract

We study slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections. We obtain general formulas for the observables: spectral indices, tensor-to-scalar ratio and circular polarization of gravitational waves. The Gauss-Bonnet term violates the consistency relation r = -8n_T. Particularly, blue spectrum n_T > 0 and scale invariant spectrum |8n_T|/r << 1 of tensor modes are possible. These cases require the Gauss-Bonnet coupling function of \xi _{,\phi } \sim 10^8/M_{Pl}. We use examples to show new-inflation-type potential with 10M_{Pl} symmetry breaking scale and potential with flat region in \phi \gtrsim 10M_{Pl} lead to observationally consistent blue and scale invariant spectra, respectively. Hence, these interesting cases can actually be realized. The Chern-Simons term produce circularly polarized tensor modes. We show an observation of these signals supports existence of the Chern-Simons coupling function of \omega _{,\phi } \sim 10^8/M_{Pl}. Thus, with future observations, we can fix or constrain the value of these coupling functions, at the CMB scale.