Abstract
Axions are pseudo-Nambu–Goldstone bosons linearly coupled to the Chern-Simons topological terms of gauge fields. Thus, they adhere to an approximate symmetry with respect to shifts in field space. Axion was originally introduced to solve the notorious "strong CP-problem" in Quantum Chromodynamics. Later it was realized that axions are generic for theories beyond the Standard Model of particle physics. Because of the shift-symmetry, axions are widely used to model early Universe Inflation and Dark Matter. These are predominantly gravitational phenomena and it is paramount to understand how axions couple to gravity. We propose a systematic study that addresses this question by examining theoretical and phenomenological implications of coupling axions to gravity non-minimally. In particular, a coupling to the gravitational Gauss-Bonnet topological term is unavoidable from the Effective Field Theory perspective. This coupling resembles the way axions couple to other gauge fields and may have profound consequences, especially in the early universe and in high curvature environments.