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 = -8 n _ { T } .
Particularly , blue spectrum n _ { T } > 0 and scale invariant spectrum | 8 n _ { T } | / r \ll 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 10 M _ { Pl } symmetry breaking scale and potential with flat region in \phi \gtrsim 10 M _ { 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 .