Power spectrum oscillations from Planck-suppressed operators in effective field theory motivated monodromy inflation

We consider a phenomenological model of inflation where the inflaton is the phase of a complex scalar field $\Phi$. Planck-suppressed operators of $\mathcal O(f^5/M_\mathrm{pl})$ modify the geometry of the vev $\langle \Phi \rangle$ at first order in the decay constant $f$, which adds a first order periodic term to the definition of the canonically normalized inflaton $\phi$. This correction to the inflaton induces a fixed number of extra oscillatory terms in the potential $V \sim \theta^p$. We derive the same result in a toy scenario where the vacuum $\langle \Phi \rangle$ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale $k$ and provide a possible mechanism for differentiating EFT-motivated inflation from models where the angular shift symmetry is a gauge symmetry.