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Relativistic Turbulence: A Long Way from Preheating to Equilibrium

R. Micha, I. I. Tkachev

TL;DR

The process is characterized by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics, and simplified kinetic theory gives values for all characteristic exponents which are close to what is observed in lattice simulations.

Abstract

We study, both numerically and analytically, the development of equilibrium after preheating. We show that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics. Simplified kinetic theory gives values for all characteristic exponents which are close to what is observed in lattice simulations. The resulting time for thermalization is long, and temperature at thermalization is low, $T \sim 100$ eV in the simple $λΦ^4$ inflationary model. Our results allow a straightforward generalization to realistic models.

Relativistic Turbulence: A Long Way from Preheating to Equilibrium

TL;DR

The process is characterized by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics, and simplified kinetic theory gives values for all characteristic exponents which are close to what is observed in lattice simulations.

Abstract

We study, both numerically and analytically, the development of equilibrium after preheating. We show that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics. Simplified kinetic theory gives values for all characteristic exponents which are close to what is observed in lattice simulations. The resulting time for thermalization is long, and temperature at thermalization is low, eV in the simple inflationary model. Our results allow a straightforward generalization to realistic models.

Paper Structure

This paper contains 7 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction.
  2. The Model.
  3. Numerical Procedure and Results.
  4. Discussion.
  5. Equilibration time and temperature.
  6. Conclusions.
  7. Acknowledgements.

Figures (3)

  • Figure 1: Amplitude of the zero-mode oscillations, $\overline\phi_0^2$, and variance of the field fluctuations as functions of time $\tau$.
  • Figure 2: Occupation numbers as function of $k\overline\phi_0^{-1}$ at $\tau = 100, 400, 2500, 5000, 10000$.
  • Figure 3: On the right hand side we plot the wave energy per decade found in lattice integration. On the left hand side are the same graphs transformed according to the relation inverse to Eq. (\ref{['SelfS']}).