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Superconformal Generalization of the Chaotic Inflation Model λφ^4/4 - ξ/ 2 φ^2 R

Renata Kallosh, Andrei Linde

TL;DR

This work embeds the chaotic inflation model with a quartic potential $V(\phi)=\frac{\lambda}{4}\phi^{4}$ and a small nonminimal coupling $-\frac{\xi}{2}\phi^{2}R$ into (super)conformal frameworks, introducing a deformation parameter $\Delta$ (related to $\xi$) that controls nonminimal gravity coupling while preserving conformal symmetry at the level of the action. It shows that conformal/superconformal invariance can be maintained with a complex scalar sector and a Goldstino multiplet, with spontaneous breaking yielding the desired inflaton dynamics and a quartic potential identical to the global theory. The authors derive the phenomenology, including the inflaton quartic coupling $\lambda$ and slow-roll observables $r$ and $n_s$, demonstrating compatibility with Planck2013 for $\xi\gtrsim2\times10^{-3}$ and discussing reheating scenarios that may distinguish visible versus hidden sector realizations. A key conceptual insight is that small $\xi$ is technically natural due to enhanced symmetry at $\xi=0$, and the framework provides a minimal, symmetry-driven path to embed inflation in supergravity. The approach yields concrete, testable predictions while preserving the underlying conformal structure, offering a versatile platform for exploring related inflationary models.

Abstract

A model of chaotic inflation based on the theory of a scalar field with potential λφ^4 perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity -ξ/2 φ^2 R with ξ> 0.002. We describe embedding of this model into the superconformal theory with spontaneous breaking of superconformal symmetry, and into supergravity. A model with small ξis technically natural: setting the small parameter ξto zero leads to a point of enhanced symmetry in the underlying superconformal theory.

Superconformal Generalization of the Chaotic Inflation Model λφ^4/4 - ξ/ 2 φ^2 R

TL;DR

This work embeds the chaotic inflation model with a quartic potential and a small nonminimal coupling into (super)conformal frameworks, introducing a deformation parameter (related to ) that controls nonminimal gravity coupling while preserving conformal symmetry at the level of the action. It shows that conformal/superconformal invariance can be maintained with a complex scalar sector and a Goldstino multiplet, with spontaneous breaking yielding the desired inflaton dynamics and a quartic potential identical to the global theory. The authors derive the phenomenology, including the inflaton quartic coupling and slow-roll observables and , demonstrating compatibility with Planck2013 for and discussing reheating scenarios that may distinguish visible versus hidden sector realizations. A key conceptual insight is that small is technically natural due to enhanced symmetry at , and the framework provides a minimal, symmetry-driven path to embed inflation in supergravity. The approach yields concrete, testable predictions while preserving the underlying conformal structure, offering a versatile platform for exploring related inflationary models.

Abstract

A model of chaotic inflation based on the theory of a scalar field with potential λφ^4 perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity -ξ/2 φ^2 R with ξ> 0.002. We describe embedding of this model into the superconformal theory with spontaneous breaking of superconformal symmetry, and into supergravity. A model with small ξis technically natural: setting the small parameter ξto zero leads to a point of enhanced symmetry in the underlying superconformal theory.

Paper Structure

This paper contains 12 sections, 72 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Conformally invariant model for real scalars
  3. A Bosonic Conformal $\Delta$-Model: Simplified Superconformal Model
  4. Enhanced symmetries of the Kähler potential of the embedding manifold
  5. Spontaneous breaking of conformal symmetry
  6. Explicit Proof of Conformal Symmetry of the Action with Arbitrary $\Delta$
  7. $\Delta$-Deformed Canonical Superconformal Supergravity Model
  8. The role of Goldstino
  9. Superconformal generalization of the model ${\lambda\over 4} \phi^4 - {\xi\over 2}\phi^2 R$
  10. Phenomenology
  11. Discussion
  12. Canonical Superconformal Supergravity Model

Figures (1)

  • Figure 1: Red stripes show inflation parameters $n_{s}$ and $r$ for the model $\lambda\phi^{4}/4$ for different values of $\xi$ in the term $\xi\phi^{2} R/2$. The top range corresponds to $\xi = 0$. Different stripes correspond to different number of e-foldings $N$. The right one corresponds to $N = 60$, the left one corresponds to $N = 50$.