Unified no-scale model of modulus fixing, inflation, supersymmetry breaking, and dark energy

John Ellis,Keith A Olive,Dimitri V Nanopoulos,Sarunas Verner

doi:10.1103/physrevd.100.025009

Abstract

We present a minimal SU(2,1)/SU(2) x U(1) no-scale model that incorporates in an economical way modulus fixing, Starobinsky-like inflation, an adjustable scale for supersymmetry breaking and the possibility of a small cosmological constant, a.k.a. dark energy.

Highlights

Physics contains many hierarchies of mass scales, starting from the Planck scale MP ∼ 1019 GeV at which the effects of quantum gravity must become important, through the energy scale of cosmological inflation, which is ≲1013 GeV, through the electroweak scale ∼100 GeV, down to the energy scale of dark energy, a.k.a. the cosmological constant, which is ∼10−3 eV
What are the origins of these hierarchies, and how can they be stabilized in a natural way despite the depredations of quantum corrections? Diverse origins have been proposed, and this paper does not claim any progress in elucidating this aspect of the hierarchies
We have outlined in this paper a simple no-scale supergravity framework for sub-Planckian physics capable of including modulus fixing, Starobinsky-like inflation at a scale Oð1013Þ GeV, supersymmetry breaking at a scale Oð103Þ GeV, and a small positive cosmological constant

Summary

INTRODUCTION

Physics contains many hierarchies of mass scales, starting from the Planck scale MP ∼ 1019 GeV at which the effects of quantum gravity must become important, through the energy scale of cosmological inflation, which is ≲1013 GeV, through the electroweak scale ∼100 GeV, down to the energy scale of dark energy, a.k.a. the cosmological constant, which is ∼10−3 eV. No-scale supergravity has been shown to yield Starobinsky-like models of inflation [7], under suitable conditions on the theoretical parameters [8], and we have recently characterized general conditions under which de Sitter (dS) vacua can be accommodated within no-scale supergravity [9] Upgrading such models to something resembling the Standard Model (SM) in a more realistic way requires a deeper discussion on how matter fields should be incorporated, that should include a mechanism for supersymmetry breaking. For a transition between two dS vacua, one that can accommodate Starobinsky-like inflation and one with an amount of vacuum energy that could be very small, like the present cosmological constant (dark energy), without invoking any external mechanism such as uplifting by fibers [16] As we show, this class of models allows for supersymmetry breaking with a magnitude suitable for stabilizing the electroweak hierarchy, without invoking any hidden sector ala Polonyi. We preview the interpretations of these expressions, before discussing them in more detail in the bulk of the paper

SUPERSYMMETRY BREAKING AND THE COSMOLOGICAL CONSTANT

INFLATIONARY DYNAMICS

STANDARD MODEL INTERACTIONS

SUMMARY