Inflation and Integrable one-field Cosmologies embedded in Rheonomic Supergravity

TL;DR

This paper demonstrates a new method to embed inflationary potentials into supergravity using geometric properties of Kahler manifolds, simplifying previous approaches and linking microscopic physics with cosmological models.

Contribution

It introduces a novel embedding strategy based on nilpotent gaugings within standard matter-coupled supergravity, avoiding auxiliary sets and conformal compensators.

Findings

All recently classified integrable potentials are embedded into supergravity.

A simple formula relates Kahler curvature to the inflation potential.

One potential fits PLANCK data well and has intriguing geometric features.

Abstract

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.