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Supernatural Inflation: Inflation from Supersymmetry with No (Very) Small Parameters

Lisa Randall, Marin Soljacic, Alan Guth

TL;DR

The paper shows that inflation can be realized within supersymmetric theories using flat-direction fields without introducing new tiny parameters. By employing a two-field hybrid mechanism, inflation ends when a moduli-like field’s mass-squared flips sign, while the energy density is set by SUSY-breaking scales, yielding a low Hubble scale $H\sim10^3$–$10^4$ GeV and a nearly scale-invariant spectrum with $n\gtrsim1$ and negligible tensor modes. A distinctive prediction is a spike in the small-scale density perturbation spectrum, compatible with current bounds on primordial black holes and gravitino production. The framework can be instantiated in MSSM or GUT extensions, and it yields testable consequences for the scalar index and the absence of significant tensor modes, along with potential observational signatures at short wavelengths.

Abstract

Most models of inflation have small parameters, either to guarantee sufficient inflation or the correct magnitude of the density perturbations. In this paper we show that, in supersymmetric theories with weak scale supersymmetry breaking, one can construct viable inflationary models in which the requisite parameters appear naturally in the form of the ratio of mass scales that are already present in the theory. Successful inflationary models can be constructed from the flat-direction fields of a renormalizable supersymmetric potential, and such models can be realized even in the context of a simple GUT extension of the MSSM. We evade naive ``naturalness" arguments by allowing for more than one field to be relevant to inflation, as in ``hybrid inflation" models, and we argue that this is the most natural possibility if inflaton fields are to be associated with flat direction fields of a supersymmetric theory. Such models predict a very low Hubble constant during inflation, of order $10^3$-$10^4$ GeV, a scalar density perturbation index $n$ which is very close to or greater than unity, and negligible tensor perturbations. In addition, these models lead to a large spike in the density perturbation spectrum at short wavelengths.

Supernatural Inflation: Inflation from Supersymmetry with No (Very) Small Parameters

TL;DR

The paper shows that inflation can be realized within supersymmetric theories using flat-direction fields without introducing new tiny parameters. By employing a two-field hybrid mechanism, inflation ends when a moduli-like field’s mass-squared flips sign, while the energy density is set by SUSY-breaking scales, yielding a low Hubble scale – GeV and a nearly scale-invariant spectrum with and negligible tensor modes. A distinctive prediction is a spike in the small-scale density perturbation spectrum, compatible with current bounds on primordial black holes and gravitino production. The framework can be instantiated in MSSM or GUT extensions, and it yields testable consequences for the scalar index and the absence of significant tensor modes, along with potential observational signatures at short wavelengths.

Abstract

Most models of inflation have small parameters, either to guarantee sufficient inflation or the correct magnitude of the density perturbations. In this paper we show that, in supersymmetric theories with weak scale supersymmetry breaking, one can construct viable inflationary models in which the requisite parameters appear naturally in the form of the ratio of mass scales that are already present in the theory. Successful inflationary models can be constructed from the flat-direction fields of a renormalizable supersymmetric potential, and such models can be realized even in the context of a simple GUT extension of the MSSM. We evade naive ``naturalness" arguments by allowing for more than one field to be relevant to inflation, as in ``hybrid inflation" models, and we argue that this is the most natural possibility if inflaton fields are to be associated with flat direction fields of a supersymmetric theory. Such models predict a very low Hubble constant during inflation, of order - GeV, a scalar density perturbation index which is very close to or greater than unity, and negligible tensor perturbations. In addition, these models lead to a large spike in the density perturbation spectrum at short wavelengths.

Paper Structure

This paper contains 11 sections, 50 equations, 3 figures.

Table of Contents

  1. Introduction
  2. One vs. Two Field Inflation
  3. Supernatural Inflation
  4. Another Model
  5. Examples of "Flat Direction" Interaction Potentials
  6. $\psi$ and $\phi$ Evolution
  7. Black Holes?
  8. Gravitino Constraint
  9. Baryogenesis
  10. Discussion
  11. Conclusion

Figures (3)

  • Figure 1: Parameter choices for supernatural inflation with $M'$ at the Planck scale. Here $\mu_\psi$ is chosen to give the correct magnitude of density fluctuations for the minimum $\mu_\psi$ consistent with a sufficiently rapid end to inflaton.
  • Figure 3: Parameters for supernatural inflation with $M'$ at the intermediate scale.
  • Figure 4: Parameter choices for supernatural inflation with renormalizable couplings, for $\lambda=10^{-4}$. Like the previous figures, this graph shows the parameters associated with the minimal allowed value of $\mu_\phi$.