Here we present supplementary online video material concerning the following publication:

**Thomas Gasenzer, Boris Nowak, and Denes Sexty**

1Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

2ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany

arXiv:1108.0541 [hep-ph]

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Videos by Dénes Sexty

The videos show a 2D simulation of the 2-component relativistic scalar field according to the O(2)-symmetric Klein-Gordon model with *λ*(*φ*_{c}*φ*_{c})^{2} non-linear interactions.

To induce the shown parametrically resonant reheating, we start our simulations from a configuration where only the zero mode of the inflaton field *φ *is populated. Fluctuating non-zero momentum modes act as seeds for the ensuing instabilities. Choosing the mass-squared *m*^{2} = 0 and *λ* > 0, which corresponds to an equilibrium configuration in the symmetric phase, subsequent oscillation of the inflaton field induces parametrically resonant exponential growth of certain modes. Scattering between these modes causes the entire spectrum to fill up.

Looking at the real-space structure of the emerging critical configuration we find patterns similar to topo- logical defects giving rise to quasi-stationary charge separation. We find a correspondence between the appearance of the strong scaling exponent and of the defect-separated charge patterns. In Figure 2 in the above paper we depict, for *d* = 2, a typical real-space configuration in the turbulent stage, plotting the modulus of the O(2) scalar field, |*Φ*(**x**,t)| = [*Φ*_{1}^{2}(**x**,t) + *Φ*_{2}^{2}(**x**,t)]^{1/2}. Localised regions appear, specifically “defect” lines where the absolute value of the field is much smaller than its average. Fig. 3 in the paper shows the corresponding charge density *ρ*(**x**,*t*) = *j*_{0}(**x**,*t*), Eq. (4). Clearly, both uniform charge and anti-charge overdensities appear within distinctly separated regions, showing only small fluctuations as compared to their bulk values. This separation of charges is confirmed by the histogram of local charge densities shown in Fig. 4 in the paper.

Video of the whole evolution from t=0 to t=10000, illustrating the slowly evolving, reconnecting defect lines. Plotted is rho, gradient energy density, charge density.

The time evolution of the defect lines and the particle number spectrum.

The bubble wall: In a 3d simulation on a 64^3 lattice, at t=1500, points with rho^2<0.05 are higlighted:

Time evolution of the 3d system from t=0 to t=4700. Points with rho^2<0.05 are highlighted.

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