Scalar potential in F(R) supergravity

TL;DR

This paper derives the scalar potential in N=1 supergravity models based on f(R) gravity, revealing conditions for no-scale models and their relevance to inflationary cosmology.

Contribution

It provides a explicit derivation of the scalar potential in F(R) supergravity and establishes conditions for no-scale models without fine-tuning.

Findings

Scalar potential expressed via a single holomorphic function.

Conditions for vanishing cosmological constant and supersymmetry breaking.

Relevance to inflationary models in supergravity and superstrings.

Abstract

We derive a scalar potential in the recently proposed N=1 supersymmetric generalization of f(R) gravity in four space-time 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 Kaehler 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.