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Super-horizon perturbations and preheating

Andrew R. Liddle, David H. Lyth, Karim A. Malik, David Wands

TL;DR

The paper investigates whether preheating after inflation can modify large-scale curvature perturbations, focusing on the simplest chaotic inflation model with a coupled reheat field. It shows that linear perturbations from the reheat field yield negligible effects on super-horizon ζ and that the dominant second-order contributions, though amplified by parametric resonance, also produce only a negligible impact on large scales due to a steep $k^3$ spectrum and early backreaction. Consequently, preheating does not undermine the standard inflationary prediction of conserved large-scale curvature perturbations in this setup. The authors also contextualize the results within broader multi-field scenarios, noting that substantial ζ variation can occur in models with light reheat fields or surviving field components, but not in the single-component, strong-preheating case treated here.

Abstract

It has recently been claimed by Bassett et al that preheating after inflation may affect the amplitude of curvature perturbations on large scales, undermining the usual inflationary prediction. We analyze the simplest model, and confirm the results of Jedamzik and Sigl and of Ivanov that in linear perturbation theory the effect is negligible. However the dominant effect is second-order in the field perturbation and we show that this too is negligible, and hence conclude that preheating has no significant influence on large-scale perturbations in this model. We briefly discuss the likelihood of an effect in other models.

Super-horizon perturbations and preheating

TL;DR

The paper investigates whether preheating after inflation can modify large-scale curvature perturbations, focusing on the simplest chaotic inflation model with a coupled reheat field. It shows that linear perturbations from the reheat field yield negligible effects on super-horizon ζ and that the dominant second-order contributions, though amplified by parametric resonance, also produce only a negligible impact on large scales due to a steep spectrum and early backreaction. Consequently, preheating does not undermine the standard inflationary prediction of conserved large-scale curvature perturbations in this setup. The authors also contextualize the results within broader multi-field scenarios, noting that substantial ζ variation can occur in models with light reheat fields or surviving field components, but not in the single-component, strong-preheating case treated here.

Abstract

It has recently been claimed by Bassett et al that preheating after inflation may affect the amplitude of curvature perturbations on large scales, undermining the usual inflationary prediction. We analyze the simplest model, and confirm the results of Jedamzik and Sigl and of Ivanov that in linear perturbation theory the effect is negligible. However the dominant effect is second-order in the field perturbation and we show that this too is negligible, and hence conclude that preheating has no significant influence on large-scale perturbations in this model. We briefly discuss the likelihood of an effect in other models.

Paper Structure

This paper contains 7 sections, 35 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Perturbation evolution
  3. Preheating
  4. The initial quantum fluctuation of the $\chi$-field
  5. Parametric resonance
  6. Change in the curvature perturbation on large scales
  7. Conclusions and discussion

Figures (1)

  • Figure 1: The power spectrum of the non-adiabatic curvature perturbation ${\cal P}_{\zeta_{{\rm nad}}}$, shown at four different times: from bottom to top $m\Delta t = 0$, $50$, $100$ and $150$. The parameters used were $g=10^{-3}$, $m=10^{-6} m_{{\rm Pl}}$ and $k_{\rm cut}=k_{\rm max}$.