Orbital Inflation & Scaling Symmetry

The Planck data reveal that the inflationary perturbations are Gaussian, adiabatic and almost scale-invariant to a high level of accuracy. A possible explanation for this observed simplicity is that inflation is driven by a single scalar field with small self-interactions. However, UV embeddings of inflation typically contain more scalar fields besides the inflaton that may participate in the inflationary dynamics. Interestingly, multi-field models with efficiently coupled light fields look a lot like single field and they are consistent with the current Planck data. The reason is that the isocurvature perturbations are the dominant source of power of the curvature perturbations. This raises the question whether a symmetry can keep the dynamics of these systems under control. To address this question we reconstruct two-field models of inflation that admit an exactly constant coupling between the perturbations and a constant mass of isocurvature perturbations. The idea is to consider inflationary trajectories that attract to the Hubble gradient flow, which we align with an isometry of the field metric. We dub this `Orbital Inflation'. As a corollary, the Hubble parameter, instead of the potential, reflects the symmetries of perturbations. More generally, for an extended class of models, we identify a scaling symmetry between background solutions that fixes the dynamics of coupled inflationary perturbations. This allows us to derive the squeezed limit of the non-Gaussian bispectrum, which we find to be slow-roll suppressed, but different from single field. These results might help to realise successful models of inflation with additional light fields