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Tuning Locked Inflation: Supergravity versus Phenomenology

Richard Easther, Justin Khoury, Koenraad Schalm

TL;DR

This paper investigates locked inflation, a two-field mechanism that can drive early-universe inflation without slow-roll and aims to reconcile it with supergravity/ string theory. It shows that a secondary saddle inflation can follow locked inflation, producing a highly scale-dependent spectrum that risks catastrophic primordial black hole formation unless the parameter η is tuned or the saddle phase lasts long enough to push dangerous modes beyond our horizon; both options constrain the parameter space as a function of the reheating scale M. The authors derive expressions for the saddle-inflation dynamics, the perturbation spectrum, and the resulting black-hole production, concluding that viable scenarios require either η ≳ 30–1500 (No Saddle Inflation) or η ≲ 0.01–2.5 with appropriate M (Long Saddle Inflation), with the latter potentially relying on the DGZ mechanism to generate the observed density perturbations. They emphasize that, in the long-saddle case, locked inflation may leave little direct observational imprint, while in multi-stage setups, features could appear in the spectrum at phase boundaries, warranting further study.

Abstract

We analyze the cosmological consequences of locked inflation, a model recently proposed by Dvali and Kachru that can produce significant amounts of inflation without requiring slow-roll. We pay particular attention to the end of inflation in this model, showing that a secondary phase of saddle inflation can follow the locked inflationary era. However, this subsequent period of inflation results in a strongly scale dependent spectrum that can lead to massive black hole formation in the primordial universe. Avoiding this disastrous outcome puts strong constraints on the parameter space open to models of locked inflation.

Tuning Locked Inflation: Supergravity versus Phenomenology

TL;DR

This paper investigates locked inflation, a two-field mechanism that can drive early-universe inflation without slow-roll and aims to reconcile it with supergravity/ string theory. It shows that a secondary saddle inflation can follow locked inflation, producing a highly scale-dependent spectrum that risks catastrophic primordial black hole formation unless the parameter η is tuned or the saddle phase lasts long enough to push dangerous modes beyond our horizon; both options constrain the parameter space as a function of the reheating scale M. The authors derive expressions for the saddle-inflation dynamics, the perturbation spectrum, and the resulting black-hole production, concluding that viable scenarios require either η ≳ 30–1500 (No Saddle Inflation) or η ≲ 0.01–2.5 with appropriate M (Long Saddle Inflation), with the latter potentially relying on the DGZ mechanism to generate the observed density perturbations. They emphasize that, in the long-saddle case, locked inflation may leave little direct observational imprint, while in multi-stage setups, features could appear in the spectrum at phase boundaries, warranting further study.

Abstract

We analyze the cosmological consequences of locked inflation, a model recently proposed by Dvali and Kachru that can produce significant amounts of inflation without requiring slow-roll. We pay particular attention to the end of inflation in this model, showing that a secondary phase of saddle inflation can follow the locked inflationary era. However, this subsequent period of inflation results in a strongly scale dependent spectrum that can lead to massive black hole formation in the primordial universe. Avoiding this disastrous outcome puts strong constraints on the parameter space open to models of locked inflation.

Paper Structure

This paper contains 7 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Locked inflation: a review
  3. Inflation After Locked Inflation
  4. Perturbation spectrum and black hole formation
  5. Consequences for locked inflation
  6. How to avoid black hole formation
  7. Discussion

Figures (2)

  • Figure 1: The curve delimits those values of $\eta$ and $M$ (GeV) that lead to saddle inflation from those that do not.
  • Figure 2: Phenomenologically allowed choices for $\eta$ and $M$ (GeV). The region "Long Saddle Inflation" corresponds to the values of $\eta$ and $M$ for which saddle inflation lasts long enough to push the dangerous range of modes outside the present horizon. Unacceptable black hole production at horizon reentry excludes the middle region.