Slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections

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 vertical bar 8n(T)vertical bar/r << 1 of tensor modes are possible. These cases require the Gauss-Bonnet coupling function of xi,phi similar to 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 greater than or similar to 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 similar to 10(8)/M-Pl. Thus, with future observations, we can fix or constrain the value of these coupling functions, at the CMB scale.