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Superconformal generalizations of the Starobinsky model

Renata Kallosh, Andrei Linde

TL;DR

The authors connect the Starobinsky inflation scenario to conformal and superconformal structures by showing that the Starobinsky potential emerges from spontaneous breaking of conformal invariance in a simple scalar-tensor theory. They then embed this mechanism into a superconformal framework with three chiral multiplets, yielding a supergravity version of Starobinsky inflation with a stable inflationary trajectory. They analyze stability conditions for extra fields using a stabilization parameter $ζ$ and discuss multiple, non-unique supergravity realizations that preserve the Starobinsky dynamics. This work clarifies how $f(R)$-type inflation can arise from symmetry principles and informs moduli stabilization considerations in supersymmetric cosmology.

Abstract

We find a way to represent the Starobinsky model in terms of a simple conformally invariant theory with spontaneous symmetry breaking. We also present a superconformal theory, which, upon spontaneous breaking of the superconformal symmetry, provides a consistent supergravity generalization of the Starobinsky model.

Superconformal generalizations of the Starobinsky model

TL;DR

The authors connect the Starobinsky inflation scenario to conformal and superconformal structures by showing that the Starobinsky potential emerges from spontaneous breaking of conformal invariance in a simple scalar-tensor theory. They then embed this mechanism into a superconformal framework with three chiral multiplets, yielding a supergravity version of Starobinsky inflation with a stable inflationary trajectory. They analyze stability conditions for extra fields using a stabilization parameter and discuss multiple, non-unique supergravity realizations that preserve the Starobinsky dynamics. This work clarifies how -type inflation can arise from symmetry principles and informs moduli stabilization considerations in supersymmetric cosmology.

Abstract

We find a way to represent the Starobinsky model in terms of a simple conformally invariant theory with spontaneous symmetry breaking. We also present a superconformal theory, which, upon spontaneous breaking of the superconformal symmetry, provides a consistent supergravity generalization of the Starobinsky model.

Paper Structure

This paper contains 5 sections, 16 equations, 1 figure.

Table of Contents

  1. Introduction
  2. de Sitter from spontaneously broken conformal symmetry
  3. Starobinsky model as a theory with spontaneously broken conformal symmetry
  4. Supersymmetry and Starobinsky model
  5. Discussion

Figures (1)

  • Figure 1: The potential of the stable supergravity generalization of the Starobinsky model with the Kähler potential (\ref{['Kquadratic']}) for $\zeta = 0$, Fig. \ref{['Star1']}, and for $\zeta = 0.5$, Fig. \ref{['Star2']}. The fields are shown in Planckian units, the height of the potential is shown in units of $\lambda = 1/9$.