Scalar potential in F (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.