de Sitter vacuum from $R^2$ supergravity

TL;DR

This paper presents a supergravity model that achieves both Starobinsky inflation and a de Sitter vacuum, with a natural hierarchy between the gravitino mass and soft SUSY breaking scale.

Contribution

It introduces a constrained curvature multiplet in supergravity to realize inflation and de Sitter vacuum simultaneously, with a novel hierarchical structure avoiding the gravitino problem.

Findings

Soft SUSY breaking scale is at TeV, suitable for MSSM.

Gravitino mass is much higher than soft SUSY breaking.

Hierarchy arises without introducing new scales beyond inflation.

Abstract

We propose a supergravity model with a constrained curvature multiplet, which realizes the Starobinsky inflation and the de Sitter vacuum in the present universe simultaneously. Surprisingly, at the vacuum, the soft supersymmetry breaking scale for minimal supersymmetric standard model sector becomes the TeV scale, however, the gravitino mass scale becomes much higher than that of soft supersymmetry breaking. Such a hierarchical structure, which naturally avoids the gravitino problem, appears without introducing a new scale other than inflation scale.