Inflation and dark energy with a single superfield

Andrei Linde,Diederik Roest,Marco Scalisi

doi:10.1088/1475-7516/2015/03/017

Abstract

We discuss the possibility to construct supergravity models with a single superfield describing inflation as well as the tiny cosmological constant V ∼ 10−120. One could expect that the simplest way to do it is to study models with a supersymmetric Minkowski vacuum and then slightly uplift them. However, due to the recently proven no-go theorem, such a tiny uplifting cannot be achieved by a small modification of the parameters of the theory. We illustrate this general result by investigation of models with a single chiral superfield recently proposed by Ketov and Terada. We show that the addition of a small constant or a linear term to the superpotential of a model with a stable supersymmetric Minkowski vacuum converts it to an AdS vacuum, which results in a rapid cosmological collapse. One can avoid this problem and uplift a supersymmetric Minkowski vacuum to a dS vacuum with V0∼ 10−120 without violating the no-go theorem by making these extra terms large enough. However, we show that this leads to a strong supersymmetry breaking in the uplifted vacua.

Highlights

We show that the addition of a small constant or a linear term to the superpotential of a model with a stable supersymmetric Minkowski vacuum converts it to an AdS vacuum, which results in a rapid cosmological collapse
In this paper we have investigated the possibility to realize a model of inflation and dark energy in supergravity
One could expect that this is a wonderful first approximation to describe dS vacua with vanishingly small vacuum energy V0 ∼ 10−120 and small supersymmetry breaking with m3/2 ∼ 10−15 or 10−13 in Planck units

Summary

Inflation and uplifting with a linear superpotential

To understand the basic features of the theories with the Kahler potential (1.1), it is instructive to calculate the coefficient G(φ, χ) in front of the kinetic term of the field Φ. One would expect higher-order corrections which might slightly perturb the potential; we focus on the effect of the lower-order terms Inflation in this models happens when the field slowly moves along the nearly flat valley and rolls down towards the minimum of the potential. Because of the large curvature of the potential in the φ direction, during inflation this field rapidly reaches an inflationary attractor trajectory and adiabatically follows the position of the minimum of the potential V (φ, χ) for any given value of the field χ(t) This can be confirmed by a numerical investigation of the combined evolution of the two fields whose dynamics is shown in figure 4. One could expect that this is a consequence of the simplicity of the model that we decided to study, but we will see that this result is quite generic

Inflation and uplifting with a quadratic superpotential

Discussion