Aspects of Wave Turbulence in Preheating
  In this work we have studied the nonlinear preheating dynamics of the $\frac{1}{4} \lambda \phi^4$ inflationary model. It is well established that after a linear stage of preheating characterized by the parametric resonance, the nonlinear dynamics becomes relevant driving the system towards turbulence. Wave turbulence is the appropriated description of this phase since matter distributions are fields instead of usual fluids. Therefore, turbulence develops due to the nonlinear interations of waves, here represented by the small inhomogeneities of the inflaton field. We present relevant aspects of wave turbulence such as the Kolmogorov-Zakharov spectrum in frequency and wave number domains that indicates that there are a transfer of energy through scales. From the power spectrum of the matter energy density we were able to estimate the temperature of the thermalized system. 
Jos\'e A. Crespo and H. P. de Oliveira
gr-qc hep-th