Patterns from preheating

The formation of regular patterns is a well-known phenomenon in condensed m atter physics. Systems that exhibit pattern formation,are typically driven and dissipative with pattern formation occurring in the weakly nonlinear re gime and sometimes even in more strongly nonlinear regions of parameter spa ce. In the early universe, parametric resonance can drive explosive particl e production called preheating. The fields that are populated then decay qu antum mechanically if their particles are unstable. Thus, during: preheatin g, a driven-dissipative system exists. Motivated by the application to cosm ology, we present a case study for pattern formation in relativistic nonlin ear wave equations.