Scalar potential in F({\cal R}) supergravity

We derive a scalar potential in the recently proposed N = 1 supersymmetric generalization of f(R) gravity in four spacetime dimensions. Any such higher-derivative supergravity is classically equivalent to the standard N = 1 supergravity coupled to a chiral (matter) superfield, via a Legendre-Weyl transform in superspace. The Kähler potential, the superpotential and the scalar potential of that theory are all governed by a single holomorphic function. We also find the conditions for the vanishing cosmological constant and spontaneous supersymmetry breaking, without fine tuning, which define a no-scale F(R) supergravity. The F(R) supergravities are suitable for physical applications in the inflationary cosmology based on supergravity and superstrings.

Supported in part by the Japanese Society for Promotion of Science (JSPS).