Orbital Inflation: inflating along an angular isometry of field space

The simplicity of the CMB data, so well described by single-field inflation, raises the question whether there might be an equally simple multi-field realization consistent with the observations. We explore the idea that an approximate angular shift symmetry in field space (an isometry) protects the dynamics of coupled inflationary perturbations. This idea relates to the recent observation that multi-field inflation mimics the predictions of single-field inflation, if the inflaton is efficiently and constantly coupled to a second massless degree of freedom (the isocurvature perturbation). In multi-field inflation, the inflationary trajectory is in general not aligned with the gradient of the potential. As a corollary the potential does not reflect the symmetries of perturbations. We propose a new method to reconstruct simultaneously a two-field action and an inflationary trajectory which proceeds along an `angular direction of field space, with a constant radius of curvature, and that has a controlled mass of `radial isocurvature perturbations (entropy mass). We dub this `Orbital Inflation. In this set-up the Hubble parameter determines the behavior of both the background and the perturbations. First, Orbital Inflation provides a playground for quasi-single field inflation. Second, the exquisite analytical control of these models allows us to exactly solve the phenomenology of Orbital Inflation with a small entropy mass and a small radius of curvature, a regime not previously explored. The predictions are single-field-like, although the consistency relations are violated. Moreover, the value of the entropy mass dictates how the inflationary predictions fan out in the ($n_s$, $r$) plane. Depending on the size of the self interactions of the isocurvature perturbations, the non-Gaussianity parameter $f_{NL}$ can range from slow-roll suppressed to $mathcal{O}(text{a few})$.