Oscillon decay via parametric resonance: the case of three-point scalar interactions

TL;DR

The paper addresses how oscillon decay through parametric resonance into an external scalar field depends on the specific form of the coupling. It extends prior results for a four-point coupling to include a three-point interaction $g_3\phi\chi^2$, and uses Floquet analysis to characterize instability bands, along with nonlinear two-field simulations under spherical symmetry. The key finding is that partial decay—where resonance halts before complete oscillon destruction and leaves a smaller remnant—emerges generically, with the precise instability structure and energy thresholds sensitive to the coupling type. This robustness has potential implications for post-inflation reheating, indicating that oscillons can mediate energy transfer without necessarily dissolving in all coupling scenarios.

Abstract

We investigate the decay dynamics of oscillons through interactions with an external scalar field. To examine how robust the decay dynamics of oscillons via parametric resonance we previously found in Li et al. 2025 are to the specific form of the coupling, we extend the analysis to include a three-point interaction $g_3φχ^2$. We compute the Floquet exponents of the external field $χ$ under an oscillating oscillon background and analyze how the instability bands depend on the coupling constants and the oscillon shapes. Numerical simulations of the two-field system show that, similar to the four-point case, the parametric resonance may cease before the oscillon is destroyed, leaving a smaller oscillon that decays only perturbatively. This indicates that the partial decay of oscillons through parametric resonance is a generic phenomenon of oscillon-scalar couplings, qualitatively insensitive to the specific interaction form, while the shape of instability bands, parameter dependence, and the precise critical oscillon energies depend on the specific coupling. Our findings provide further insights into the decay dynamics of oscillons and their potential role in the post-inflationary reheating process.

Figures (9)

• Figure 1: Left panel: Oscillon profiles solved numerically for $\omega/m_\phi= 0.80$ and $\omega/m_\phi= 0.94$, with $m_\phi^2 \lambda_6/\lambda^2 = 0.8$. The corresponding charges $I$ are computed by the integral of profile as given by Eq. \ref{['eq:adiabatic charge']}. Right panel: The dependence of the oscillon charge and energy on its fundamental frequency $\omega$, obtained by solving Eq. \ref{['eq:eom oscillon profile']} for different values of $\omega$ with $m_\phi^2 \lambda_6/\lambda^2 = 0.8$, and integrating Eq. \ref{['eq:adiabatic charge']} and Eq. \ref{['eq:time-average energy from oscillon profile']}. The red dashed lines are the critical values of $\omega_{\text{death}}/m_\phi = 0.96$ and $\lambda I_{\text{death}} = 17.48$ for "energetic death", beyond which the oscillon solution is no more stable against perturbations. We define the end of the oscillon lifetime as the moment when oscillon reaches this critical value.
• Figure 2: Floquet charts of the Mathieu equation in Eq. \ref{["eq:standard Mathieu's eq"]} neglecting oscillon inhomogeneity, shown in the $(k, g_3)$ plane. The oscillon center amplitude $\psi_0$ corresponds to $\omega/m_\phi = 0.8$. Left and right panels: $m_\chi/m_\phi = 0.3$ and $0.6$, respectively. Dashed line: $g_3 = 0$.
• Figure 3: The maximum value of the real part of Floquet exponents, $\mu_{\max} \equiv \max{(\Re{(\mu)})}$, representing the growth rate of the most unstable mode, is shown for various coupling strengths $g_3/(m_\phi\sqrt{\lambda})$ and mass $m_\chi/m_\phi$. The center amplitude $\psi_0 (\simeq 0.46 m/\sqrt{\lambda})$ and frequency of an oscillon with $\omega/m_\phi = 0.8$ are used in the computation. The dashed line denotes the linear dependence in the first narrow resonance band, $\mu_{\max} = |q|/2$, while the dot-dashed line indicates the quadratic dependence in the second narrow band, $\mu_{\max} = q^2/16$.
• Figure 4: Growth rate of the $\chi$ field obtained from numerical simulations with a fixed oscillon background of $\omega/m_\phi = 0.8$, for various values of $m_\chi$. The black dashed line shows the corresponding $\mu_{\max}$ from the homogeneous Floquet analysis presented in the previous subsection, for comparison.
• Figure 5: Normalized Fourier spectrum of the center value of $\widetilde{\chi}$, $\widetilde{\chi}(\widetilde{t},0)$, obtained from simulations with a fixed oscillon background $\widetilde{\phi}(\widetilde{t},\widetilde{r})$ for $\omega/m_\phi = 0.8$. Dashed lines indicate the half-integer multiples of the background frequency, $n\omega/2$.