Parametric Resonance in $\phi^4$ Preheating: An Exact Numerical Study

TL;DR

This paper provides a detailed numerical analysis of parametric resonance during preheating in a $^4$ inflation model, revealing complex, coupling-dependent resonance patterns that differ from previous analytical approximations.

Contribution

It offers the first exact numerical study of resonance structures in $^4$ preheating, avoiding common approximations and uncovering new dynamical behaviors.

Findings

Resonance patterns differ significantly from analytical predictions.

Weak coupling modes reach saturation quickly, long-wavelength modes grow gradually.

Strong coupling induces stochastic and staircase-like particle production behaviors.

Abstract

Preheating after inflation proceeds through parametric resonance, leading to efficient particle production in scalar field models. In this work, we investigate the structure of parametric resonance in the $\phi^4$ chaotic inflationary model during the preheating phase by performing a fully numerical analysis of the coupled dynamical equations governing the inflaton field and the mode function of the produced particles, thereby avoiding the approximations commonly employed in earlier studies. Our results reveal resonance patterns that differ significantly from those obtained with approximate analytical treatments. In the weak coupling regime, short-wavelength modes rapidly settle into oscillations with nearly constant amplitude, while the corresponding occupation numbers approach saturation. However, the long-wavelength modes exhibit gradual amplitude growth, with occupation numbers transitioning into a non-linear oscillatory regime. As the coupling strength increases, the dynamics becomes increasingly nonlinear, leading to the emergence of stochastic behavior. In the strong coupling regime, short-wavelength modes display a step-like (staircase) evolution in the occupation number, indicative of intermittent bursts of particle production. However, the long-wavelength modes exhibit a more gradual, monotonic growth with small superimposed fluctuations. These findings highlight the rich, coupling-dependent, structure of parametric resonance in the quartic inflationary model and underscore the importance of exact numerical treatment in accurately capturing preheating dynamics.