Inflation in $R^2$ supergravity with non-minimal superpotentials

TL;DR

This paper explores how adding specific superpotential terms in supergravity models generalizing $R^2$ inflation affects the scalar potential and inflationary predictions, including the tensor-to-scalar ratio, with implications for recent observational data.

Contribution

It introduces new superpotential terms quadratic in the superfield, significantly modifying the scalar potential and inflationary outcomes in supergravity $R^2$ models.

Findings

The scalar potential becomes an exponential factor times the Starobinsky potential.

Starobinsky inflation persists only with fine-tuned superpotential couplings.

The tensor-to-scalar ratio $r$ can be increased within observational limits.

Abstract

We investigate the cosmological inflation in a class of supergravity models that are generalizations of non-supersymmetric $R^2$ models. Although such models have been extensively studied recently, especially after the launch of the PLANCK and BICEP2 data, the class of models that can be constructed has not been exhausted. In this note, working in a supergravity model that is a generalization of Cecotti's model, we show that the appearance of new superpotential terms, which are quadratic in the superfield $\, \Lambda$ that couples to the Ricci supermultiplet, alters substantially the form of the scalar potential. The arising potential has the form of the Starobinsky potential times a factor that is exponential in the inflaton field and dominates for large inflaton values. We show that the well-known Starobinsky inflation scenario is maintained only for unnaturally small fine-tuned values of the coupling describing the $\Lambda^2$ superpotential terms. A welcome feature is the possible increase of the tensor to scalar ratio $r$, within the limits set by the new Planck and BICEP2 data.