K-Oscillons: Oscillons with Non-Canonical Kinetic Terms

TL;DR

This work extends the oscillon paradigm to scalar field theories with non-canonical kinetic terms by deriving a small-amplitude existence condition $\Delta = \xi_2 - \lambda_4 + \frac{10}{9}\lambda_3^2 > 0$ and solving for oscillon profiles in $d+1$ dimensions. Via a controlled $\epsilon$-expansion, it yields an exact 1+1 dimensional k-oscillon $\varphi(t,r) \approx \varepsilon \sqrt{\frac{8}{3\Delta}}\operatorname{sech}(\varepsilon r)\cos(\tau)$ and an accurate 3+1 dimensional approximation, both governed by the nonlinear profile equation $\partial_\rho^2 f(\rho) + \frac{d-1}{\rho}\partial_\rho f(\rho) - f(\rho) + \frac{3}{4}\Delta f^3(\rho) = 0$. The stability analysis, following a Vakhitov-Kolokolov–type criterion, shows that oscillons are stable to long-wavelength perturbations for $d = 1,2$ but exhibit a long-wavelength instability for $d > 2$, with the criterion $\frac{dN}{d\varepsilon} > 0$ where $N = \varepsilon^{2-d}\int f^2(\rho) d^d\rho$. The paper also discusses radiating tails in expanding backgrounds and estimates the associated energy loss, linking these results to potential cosmological roles during preheating or dark-energy dynamics. Overall, it significantly broadens the landscape of oscillon solutions by incorporating non-canonical kinetics and sets the stage for further studies of large-amplitude, Floquet, and quantum aspects in cosmological settings.

Abstract

Oscillons are long-lived, localized, oscillatory scalar field configurations. In this work we derive a condition for the existence of small-amplitude oscillons (and provide solutions) in scalar field theories with non-canonical kinetic terms. While oscillons have been studied extensively in the canonical case, this is the first example of oscillons in scalar field theories with non-canonical kinetic terms. In particular, we demonstrate the existence of oscillons supported solely by the non-canonical kinetic terms, without any need for nonlinear terms in the potential. In the small-amplitude limit, we provide an explicit condition for their stability in d+1 dimensions against long-wavelength perturbations. We show that for d > 2, there exists a long-wavelength instability which can lead to radial collapse of small-amplitude oscillons.