Inflation and Integrable one-field Cosmologies embedded in Rheonomic
  Supergravity
  In this paper we show that the new approach to the embedding of the
inflationary potentials into supergravity, presented in a quite recent paper
[11] of Ferrara, Kallosh, Linde and Porrati can be formulated within the
framework of standard matter coupled supergravity, without the use of the new
minimal auxiliary set and of conformal compensators. The only condition is the
existence of a translational Peccei Quinn isometry of the scalar Kahler
manifold. We suggest that this embedding strategy based on a nilpotent gauging
amounts to a profound Copernican Revolution. The properties of the inflaton
potential are encoded in the geometry of some homogeneous one-dimensional
Kahler manifolds that now should be regarded as the primary object, possibly
providing a link with microscopic physics. We present a simple and elegant
formula for the curvature of the Kahler manifold in terms of the potential.
Most relevant consequence of the new strategy is that all the integrable
potentials quite recently classified in a paper [7] that we have coauthored,
are automatically embedded into supergravity and their associated Kahler
manifolds demand urgent study. In particular one integrable potential that
provides the best fit to PLANCK data seems to have inspiring geometrical
properties deserving further study.
