  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.
