\(\alpha\)-attractor-type Double Inflation

Abstract

In \(\alpha\)-attractor-type double inflation. The model is composed of two minimally coupled scalar fields, where each of the field has a potential of the \(\alpha\)-attractor-type. We find that the background trajectory in this double inflation model is given by two almost straight lines connected with a turn in the field-space. With this simple background, we can classify the property of the perturbations generated in this double inflation model just depending on whether the turn occurs before the horizon exit for the mode corresponding to the scale of interest or not. In the former case, the resultant primordial curvature perturbation coincides with the one obtained by the single-field \(\alpha\)-attractor. On the other hand, in the latter case, it is affected by the multi-field effects, like the mixing with the isocurvature perturbation and the change of the Hubble expansion rate at the horizon exit. We obtain the approximated analytic solutions for the background, with which we can calculate the primordial curvature perturbation by the \(\delta N\)-formalism analytically, even when the multi-field effects are significant. We also impose observational constraints on the model parameters and initial values of the fields in this double inflation model based on the Planck result.