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

TL;DR

This paper explores how Gauss-Bonnet and Chern-Simons corrections influence slow-roll inflation, predicting observable effects like tensor polarization and deviations from standard consistency relations, with potential for future empirical constraints.

Contribution

It derives general formulas for inflation observables with these corrections and demonstrates their implications for spectral indices, polarization, and potential observational signatures.

Findings

Gauss-Bonnet term violates the standard consistency relation r = -8n_T.

Blue and scale-invariant tensor spectra are possible with specific coupling functions.

Chern-Simons term induces circular polarization in gravitational waves.

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.