# Projects: Charge separation near a non-thermal fixed point

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

## Charge separation in Reheating after Cosmological Inflation

**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

New aspects of parametrically resonant heating of a relativistic scalar O(2)-symmetric self-interacting field are presented. This process is a candidate for reheating at the end of the early-universe epoch of inflation. Although a model with a fully O(2)-symmetric ground state is used, transient, metastable spontaneous symmetry breaking can be observed. This manifests itself in the form of persistent regimes of opposite and, inside these, uniform charge overdensities separated by thin lines and walls similar to topological defects, in two and three spatial dimensions, respectively. The configuration is found to correspond to an attractive non-equilibrium fixed point of the underlying dynamic equations which prevents thermalisation over an extended period of time.

arXiv:1108.0541 [hep-ph]

## Supplementary Material

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Videos by Dénes Sexty

## Videos: Time evolution of the 2D relativistic scalar O(2) field

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.