D-Oscillons in the Standard Model-Extension

In this work we investigate the consequences of the Lorentz symmetry violation on extremely long-living, time-dependent, and spatially localized field configurations, named oscillons. This is accomplished in ($D+1$) dimensions for two interacting scalar field theories in the so-called Standard Model-Extension context. We show that $D$-dimensional scalar field lumps can present a typical size $R_{\min }\ll R_{KK}$, where $R_{KK}$ is the associated length scale of extra dimensions in Kaluza-Klein theories. Here, the size $R_{\min }$ is shown to strongly depend on the terms that control the Lorentz violation of the theory. This implies either contraction or dilation of the average radius $R_{\min}$, and a new rule for its composition, likewise. Moreover, we show that the spatial dimensions for existence of oscillating lumps have an upper limit, opening new possibilities to probe the existence of a $D$ -dimensional oscillons at TeV energy scale. Moreover, in a cosmological scenario with Lorentz symmetry breaking, we argue that in the early Universe with an extremely high energy density and a strong Lorentz violation, the typical size $R_{\min }$ was highly dilated. With the expansion and subsequent cooling of the Universe, we propose that it passed through a phase transition towards a Lorentz symmetry, wherein $R_{\min }$ tends to be compact.