The Development of Equilibrium After Preheating

TL;DR

The paper investigates how the universe thermalizes after inflation, focusing on the nonlinear dynamics of scalar fields during and after preheating using three-dimensional lattice simulations. It finds that preheating generically produces highly infrared-dominated occupation numbers and a turbulent stage where energy cascades to higher momenta, gradually approaching approximate thermal equilibrium within groups of fields coupled together. The authors formulate empirical rules for thermalization that hold across chaotic and hybrid inflation models, and analyze chaos onset via Lyapunov exponents. These results illuminate a robust pathway from preheating to a hot, thermalized early universe with implications for reheating temperatures and subsequent cosmological evolution.

Abstract

We present a fully nonlinear study of the development of equilibrium after preheating. Preheating is the exponentially rapid transfer of energy from the nearly homogeneous inflaton field to fluctuations of other fields and/or the inflaton itself. This rapid transfer leaves these fields in a highly nonthermal state with energy concentrated in infrared modes. We have performed lattice simulations of the evolution of interacting scalar fields during and after preheating for a variety of inflationary models. We have formulated a set of generic rules that govern the thermalization process in all of these models. Notably, we see that once one of the fields is amplified through parametric resonance or other mechanisms it rapidly excites other coupled fields to exponentially large occupation numbers. These fields quickly acquire nearly thermal spectra in the infrared, which gradually propagates into higher momenta. Prior to the formation of total equilibrium, the excited fields group into subsets with almost identical characteristics (e.g. group effective temperature). The way fields form into these groups and the properties of the groups depend on the couplings between them. We also studied the onset of chaos after preheating by calculating the Lyapunov exponent of the scalar fields.

Figures (23)

• Figure 1: Number density $n$ for $V = {1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2$. The plots are, from bottom to top at the right of the figure, $n_\phi$, $n_\chi$, and $n_{tot}$. The dashed horizontal line is simply for comparison. The end of exponential growth and the beginning of turbulence (i.e. the moment $t_*$) occurs around the time when $n_{tot}$ reaches its maximum.
• Figure 2: Evolution of the spectrum of $\chi$ in the model $V = {1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2$. Red plots correspond to earlier times and blue plots to later ones. For black and white viewing: The sparse, lower plots all show early times. In the thick bundle of plots higher up the spectrum is rising on the right and falling on the left as time progresses.
• Figure 3: Variances for $V = {1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2$. The upper plot shows $\langle\left(\phi-\bar{\phi}\right)^2\rangle$ and the lower plot shows $\langle\left(\chi-\bar{\chi}\right)^2\rangle$.
• Figure 4: Effective masses for $V = {1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2$ as a function of time in units of comoving momentum. The lower plot is $m_\phi$ and the upper one is $m_\chi$.
• Figure 5: Time evolution of the effective masses for the model $V = {1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2 + {1 \over 2} h^2 \chi^2 \sigma^2$. From bottom to top on the right hand side the plots show $m_\phi$, $m_\sigma$, and $m_\chi$.