Elliptic Inflation: Generating the curvature perturbation without slow-roll

There are many inflationary models in which inflaton field does not satisfy the slow-roll condition. In such models, it is difficult to generate the curvature perturbation during inflation. Thus, to generate the curvature perturbation, one must introduce another component to the theory. To cite a case, curvatons may generate dominant part of the curvature perturbation after inflation. However, we have a question whether it is unrealistic to consider the generation of the curvature perturbation during inflation without slow-roll. Assuming multi-field inflation, we encounter the generation of the curvature perturbation during inflation without slow-roll. This idea can be used to solve the serious eta-problem that arises in brane inflationary models.