We consider higher derivative supergravities that are dual to ghost-free N = 1 supergravity theories in the Einstein frame. The duality is implemented by deforming the Kähler function, and/or the superpotential, to include nonlinear dependences on chiral fields that in other approaches play the role of the Lagrange multipliers employed to establish this duality. These models are of the no-scale type, and in the minimal case, require the presence of four chiral multiplets, with a Kähler potential having the structure of the SU (4, 1)/SU (4) × U (1) coset manifold. In the standard N = 1 supergravity formulation, these models are described by a multifield scalar potential, featuring Starobinsky-like behavior in particular directions.
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 Λ 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 Λ 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.
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