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Double Field Inflation

Fred C. Adams, Katherine Freese

TL;DR

This paper tackles how to end inflation via a first-order phase transition by introducing a two-field framework in which a slowly rolling field $\psi$ modulates the nucleation rate of true-vacuum bubbles for the inflaton $\phi$. The key idea is a time-dependent nucleation rate, quantified by $\beta=\Gamma_N/\chi^4$, enabling periods of inflation with subcritical nucleation that later become supercritical to achieve percolation and completion. It demonstrates that bubble percolation and interior thermalization are more plausible under this mechanism and that achieving a sufficiently flat potential for the rolling field imposes a fine-tuning similar to that of new inflation (e.g., $\lambda_2\sim 10^{-15}$). The model can accommodate variants such as Coleman–Weinberg-type potentials and hints at natural ways to realize flat potentials, including pseudo-Nambu-Goldstone boson scenarios, while offering a distinct path to generate large-scale structure via the nucleation dynamics and potential cosmic-string production at the end of inflation.

Abstract

We present an inflationary universe model which utilizes two coupled real scalar fields. The inflation field $φ$ experiences a first order phase transition and its potential dominates the energy density of the Universe during the inflationary epoch. This field $φ$ is initially trapped in its metastable minimum and must tunnel through a potential barrier to reach the true vacuum. The second auxiliary field $ψ$ couples to the inflaton field and serves as a catalyst to provide an abrupt end to the inflationary epoch; i.e., the $ψ$ field produces a time-dependent nucleation rate for bubbles of true $φ$ vacuum. In this model, we find that bubbles of true vacuum can indeed percolate and we argue that thermalization of the interiors can more easily take place. The required degree of flatness (i.e., the fine tuning) in the potential of the $ψ$ field is comparable to that of other models which invoke slowly rolling fields. Pseudo Nambu-Goldstone bosons may naturally provide the flat potential for the rolling field.

Double Field Inflation

TL;DR

This paper tackles how to end inflation via a first-order phase transition by introducing a two-field framework in which a slowly rolling field modulates the nucleation rate of true-vacuum bubbles for the inflaton . The key idea is a time-dependent nucleation rate, quantified by , enabling periods of inflation with subcritical nucleation that later become supercritical to achieve percolation and completion. It demonstrates that bubble percolation and interior thermalization are more plausible under this mechanism and that achieving a sufficiently flat potential for the rolling field imposes a fine-tuning similar to that of new inflation (e.g., ). The model can accommodate variants such as Coleman–Weinberg-type potentials and hints at natural ways to realize flat potentials, including pseudo-Nambu-Goldstone boson scenarios, while offering a distinct path to generate large-scale structure via the nucleation dynamics and potential cosmic-string production at the end of inflation.

Abstract

We present an inflationary universe model which utilizes two coupled real scalar fields. The inflation field experiences a first order phase transition and its potential dominates the energy density of the Universe during the inflationary epoch. This field is initially trapped in its metastable minimum and must tunnel through a potential barrier to reach the true vacuum. The second auxiliary field couples to the inflaton field and serves as a catalyst to provide an abrupt end to the inflationary epoch; i.e., the field produces a time-dependent nucleation rate for bubbles of true vacuum. In this model, we find that bubbles of true vacuum can indeed percolate and we argue that thermalization of the interiors can more easily take place. The required degree of flatness (i.e., the fine tuning) in the potential of the field is comparable to that of other models which invoke slowly rolling fields. Pseudo Nambu-Goldstone bosons may naturally provide the flat potential for the rolling field.

Paper Structure

This paper contains 8 sections, 63 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Basic Mechanism
  3. Double Field Inflation
  4. The Model
  5. Constraints on the Model
  6. A simple example: The ramp potential
  7. Evolution of the Probability Function
  8. Discussion

Figures (2)

  • Figure 1: Potential energy density of inflaton field $\phi$ as a function of field strength. The energy difference $\epsilon$ between the false vacuum (at $\phi_- = -a$) and the true vacuum (at $\phi_+ =a$) provides the vacuum energy density for inflation.
  • Figure 2: Probability $p$ of a point in space being in the false vacuum as a function of nondimensional time $\tau$. Solid curve shows the double-field inflation model of Sec. III; for comparison, the dashed curve shows the case of constant nucleation efficiency (as in old inflation).