Turbulent Thermalization

TL;DR

<3-5 sentence high-level summary> Turbulent Thermalization develops a unified framework for understanding how coherent inflaton oscillations decay into a turbulent, self-similar bath of classical waves that eventually thermalize. The authors combine lattice simulations of scalar field models with wave kinetic theory to identify three stages—parametric resonance, driven stationary turbulence, and free turbulence—and derive scaling exponents for the energy/particle cascades and self-similar evolution. They show that the late-time spectra follow universal power laws consistent with weak wave turbulence, enabling parametric estimates of reheating time and temperature in Minkowski and Friedmann backgrounds. The results illuminate how energy is redistributed across momentum space and highlight the conditions under which a kinetic approach remains valid, with important implications for baryogenesis, dark matter production, and the early-universe thermal history.

Abstract

We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our prime motivation and application of the results. We identify three different stages of these processes. During the initial stage of ``parametric resonance'', only a small fraction of the initial inflaton energy is transferred to fluctuations in the physically relevant case of sufficiently large couplings. A major fraction is transfered in the prompt regime of driven turbulence. The subsequent long stage of thermalization classifies as free turbulence. During the turbulent stages, the evolution of particle distribution functions is self-similar. We show that wave kinetic theory successfully describes the late stages of our lattice calculation. Our analytical results are general and give estimates of reheating time and temperature in terms of coupling constants and initial inflaton amplitude.

Figures (11)

• Figure 1: Squared amplitude of the zero-mode oscillations, $\overline\phi_0^2$, and variance of the field fluctuations as functions of time $\eta$.
• Figure 2: Occupation numbers as function of $k/\overline\phi_0$ at $\eta = 100, 400, 2500, 5000, 10000$.
• Figure 3: On the right hand side we plot the wave energy per decade found in lattice integration at $\eta = 3600, 5100, 7000, 10000$. On the left hand side are the same graphs transformed according to the relation inverse to Eq. (\ref{['SelfS']}).
• Figure 4: Particle distributions in the self-similar regime for $h=10g$ as functions of the corresponding wave kinetic energies rescaled by the current zero-mode amplitude $\bar{\phi}_{0}$.. Upper and lower panels correspond to $\chi$ and $\phi$ fields respectively. In both cases from left to right the plots are taken at $\eta=1000,1500,2000$.
• Figure 5: Spectral energy distributions for $\chi$ (upper panel) and $\phi$ (lower panel) in the model with $h = 10 g$. In each panel we plot the wave energy per decade found in lattice integrations at three moments of time, $\eta=1000$, $1500$ and $2000$. In the lower-left corner of each panel are the same graphs transformed according to the relation inverse to Eq. (\ref{['SelfS']}).