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Ekpyrotic collapse with multiple fields

Kazuya Koyama, David Wands

TL;DR

The paper investigates ekpyrotic collapse with multiple fields and shows that a scaling solution with steep negative exponential potentials can produce a scale-invariant spectrum of isocurvature perturbations via a tachyonic entropy mode. However, this scaling solution is a phase-space saddle, not a true attractor, with a late-time attractor corresponding to single-field ekpyrotic collapse that yields a blue isocurvature spectrum. To convert these perturbations into curvature perturbations and recover a viable cosmology, the authors argue for a preceding homogeneity phase, a mechanism to convert isocurvature to curvature perturbations, and a subsequent bounce, implying a multi-phase history. The work highlights the role of phase-space structure and tachyonic instabilities in shaping primordial perturbations within ekpyrotic frameworks.

Abstract

A scale invariant spectrum of isocurvature perturbations is generated during collapse in the scaling solution in models where two or more fields have steep negative exponential potentials. The scale invariance of the spectrum is realised by a tachyonic instability in the isocurvature field. We show that this instability is due to the fact that the scaling solution is a saddle point in the phase space. The late time attractor is identified with a single field dominated ekpyrotic collapse in which a steep blue spectrum for isocurvature perturbations is found. Although quantum fluctuations do not necessarily to disrupt the classical solution, an additional preceding stage is required to establish classical homogeneity.

Ekpyrotic collapse with multiple fields

TL;DR

The paper investigates ekpyrotic collapse with multiple fields and shows that a scaling solution with steep negative exponential potentials can produce a scale-invariant spectrum of isocurvature perturbations via a tachyonic entropy mode. However, this scaling solution is a phase-space saddle, not a true attractor, with a late-time attractor corresponding to single-field ekpyrotic collapse that yields a blue isocurvature spectrum. To convert these perturbations into curvature perturbations and recover a viable cosmology, the authors argue for a preceding homogeneity phase, a mechanism to convert isocurvature to curvature perturbations, and a subsequent bounce, implying a multi-phase history. The work highlights the role of phase-space structure and tachyonic instabilities in shaping primordial perturbations within ekpyrotic frameworks.

Abstract

A scale invariant spectrum of isocurvature perturbations is generated during collapse in the scaling solution in models where two or more fields have steep negative exponential potentials. The scale invariance of the spectrum is realised by a tachyonic instability in the isocurvature field. We show that this instability is due to the fact that the scaling solution is a saddle point in the phase space. The late time attractor is identified with a single field dominated ekpyrotic collapse in which a steep blue spectrum for isocurvature perturbations is found. Although quantum fluctuations do not necessarily to disrupt the classical solution, an additional preceding stage is required to establish classical homogeneity.

Paper Structure

This paper contains 8 sections, 46 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Homogeneous field dynamics
  3. Perturbations
  4. Scaling solution
  5. Single-field dominated solution
  6. Kinetic-dominated solution
  7. Discussion
  8. Appendix

Figures (1)

  • Figure 1: Phase space trajectories around the fixed point B in three dimensional phase space spanned by $(x_1,x_2, y_1)$. We see that the single field fixed points $B_1$ and $B_2$ are late time attractors and the scaling solution $B$ is a saddle point. We take $c_1 =6$ and $c_2 =4$.Then the fixed points are given by $B_1: (2.45, 0, -2.24)$, $B_2: (0, 1.63, 0)$ and $B: (0.75, 1.13, -0.51)$.