No-scale Supergravity, Inflation, and Dark Matter

Abstract

After reviewing the motivations for cosmological inflation formulated in the formalismof supersymmetry, we argue that the appropriate framework is that of no-scale supergravity. We first discuss how to realize the most viable model of cosmic inflation, which is known as the Starobinsky model of inflation, in the context of no-scale supergravity. The Starobinsky model is based on R + R2 gravity and predicts the scalar tilt value of ns ∼ 0.965 and the tensor-to-scalar ratio r ∼ 0.0035 for 55 e-folds of inflation, as favored by Planck, WMAP, and BICEP/Keck data on the cosmic microwave background (CMB). We then show that several different no-scale supergravity models yield the Starobinsky model of inflation and that all these models are equivalent to each other and arise from the underlying symmetry properties of supergravity. We discuss generalized no-scale models, Minkowski and de Sitter solutions, and supersymmetry breaking. We then show how to construct unified no-scale models of inflation, that unify modulus fixing, supersymmetry breaking, and a small cosmological constant. We develop phenomenological and cosmological aspects of these no-scale attractor models that underpin their physical applications and discuss cosmological constraints from entropy considerations. Finally, we use the recent BICEP/Keck data on the CMB to constrain the attractor models of inflation as formulated in no-scale supergravity.