Decay and lifetime of oscillons coupled to an external scalar field: Insights from instability band analysis

TL;DR

The paper investigates how coupling an oscillon to an external scalar field χ via a four-point interaction g φ^2 χ^2 affects oscillon decay and lifetime. It combines instability-band analysis (Floquet/Martiu) of χ in both homogeneous and inhomogeneous oscillon backgrounds with full two-field simulations to capture backreaction effects. Key findings include regime-dependent resonance behavior, suppression of parametric resonance for small/compact oscillons, and a two-stage decay where χ growth is followed by single-field oscillon decay once χ ceases to grow; the residual oscillon energy is bounded by instability-band structures. These results imply that oscillons can be long-lived across a broad range of couplings, with potential implications for reheating and early-universe cosmology.

Abstract

Oscillons are long-lived, spherically symmetric solitons that can arise in real scalar field theories with potentials shallower than quadratic ones. They are considered to form via parametric resonance during the preheating stage after inflation and have extended lifetimes. However, the estimation of their lifespan becomes complicated when taking into account the interactions between the inflaton field and other fields, as naturally expected in realistic reheating scenarios. In this study, we investigate how the lifetime of a single oscillon is affected by the coupling to the external real scalar field. By numerically computing the instability bands of the external field with the inhomogeneous oscillon profile as background, we show that the resonance behavior depends intricately on the coupling strength and shape of the oscillon. We analyze distinct instability mechanisms that dominate across different regimes of the coupling strength and oscillon shapes. Especially, we show that the parametric resonance fails to occur when the oscillon size is too limited to drive enhancement of the external field. Furthermore, our simulations show that as the oscillon loses energy, the exponential growth of the external field can terminate before the oscillon reaches its critical energy for collapse, which indicates that the external field does not necessarily lead to rapid destruction of oscillons even in the presence of strong coupling or with large amplitudes. These results suggest that oscillons can remain long-lived across a wide range of coupling strengths, with potential implications for their role in cosmological evolution.

Figures (15)

• Figure 1: Left panel: Oscillon profiles solved numerically for $\omega/m= 0.85$ and $\omega/m= 0.94$, with $m^2 g_6/\lambda^2 = 16/15$. The corresponding charges $I$ are computed by the integral of the profile as given by Eq. \ref{['eq:spherical adiabatic charge']}. Right panel: The dependence of the oscillon profile shape on the fundamental frequency $\omega$, characterized by radius and amplitude at the center. It is shown that neither the radius nor the amplitude is a monotonic function of $\omega$, which implies the shape change of oscillon profile is not a monotonic pattern during the whole life of a large oscillon with an initial large charge. The red dashed lines are the critical values of $\omega_{\text{death}}/m = 0.97$ and $\lambda I_{\text{death}} = 20.07$ 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, as used in Section \ref{['subsec:decay and lifetime']}.
• Figure 2: The relation between the charge and energy of an oscillon and its fundamental frequency $\omega$, obtained by solving Eq. \ref{['eq:eom oscillon profile']} for different values of $\omega$ with $m^2 g_6/\lambda^2 = 16/15$, and integrating Eq. \ref{['eq:spherical adiabatic charge']} and Eq. \ref{['eq:time-average energy from oscillon profile']}. The red dashed lines indicate the critical values of $\omega_{\text{death}}/m = 0.97$ and $\lambda I_{\text{death}} = 20.07$ for "energetic death".
• Figure 3: Left panel: numerical decay of the single-field oscillon charge with time, starting from different initial $\omega$ with $g_6/\lambda = 16/15$. The red dashed line denotes the critical value $\overline{E}_{\textrm{death}}$ of the "energetic death". Right panel: the energy decay rate $\Gamma_\xi$ at different energy $E$, obtained from numerical simulation.
• Figure 4: Floquet charts for Mathieu's equation in Eq. \ref{["eq:standard Mathieu's eq"]} neglecting oscillon inhomogeneity in terms of $k$ and $g$, with the center amplitude of an oscillon whose $\omega/m = 0.85$ is taken for $\psi_0$. The left and right panel are when $m_\chi/m = 0$ and $m_\chi/m = 0.6$, respectively. The dashed line is where $g=0$.
• Figure 5: The maximum value of the real part of Floquet exponents $\mu_{\max} \equiv \max{(\Re{(\mu)})}$ among all the modes with various $k$, which is the growth rate of the mode that grows fastest, for various values of coupling strength $g/\lambda$ and $m_\chi/m$. The center amplitude $\psi_0 (\simeq 0.4 m/\sqrt{\lambda})$ and frequency of an oscillon with $\omega/m = 0.85$ are used in the computation. The dashed black line is the linear relation in the first narrow band, $\mu_{\max} = |q|/2$, and the grey dot-dashed line is the square root relation in the tachyonic band for $m_\chi/m = 0$, $\mu_{\max} = 2 \psi_0\sqrt{|g|}/\omega$.