Numerical Studies of Out-of-Equilibrium Processes in the Early Universe

Abstract

This thesis presents efforts to better understand out-of-equilibrium processes in the early universe. Although most of the time the universe was in thermal equilibrium, out-of-equilibrium processes are an important aspect of its evolution. For example, out-of-equilibrium processes are required for the explanation of the observed matter-antimatter asymmetry and provide signatures for gravitational wave signals from first order phase transitions in the early universe. Applications of non-equilibrium quantum field theory require approximations, as the equations of motion are generally too complicated to be solved. Currently, classical-statistical approximation to quantum dynamics and effective action approaches are the main methods for conducting numerical studies of out-of-equilibrium processes.

This thesis is based on three publications within these topics. After an introduction to cosmology and non-equilibrium quantum field theory, the publications are presented in the form of chapters. In the first, the dynamics of first order phase transitions through the nucleation of bubbles is discussed and contrasted with the decay of a false vacuum. Although both have, to some degree, an overlapping formalism for perturbative calculations, it is shown that the false vacuum decay cannot be modeled through classical dynamics, as it is a quantum effect. In the second, tachyonic preheating is studied in an effective action approach which allows to study particle production and the subsequent thermalization stage in one framework. Among other things, a parameter scan of the main results is presented and the dynamical emergence of the equation of state is shown. In the third publication, aspects of the effective action approach are studied. In particular, the damping rate in a thermal state in the loop and 1/𝑁𝑁 expansion are compared over a range of parameters. Additionally, by taking the classical limit, a comparison with the exact dynamics of classical-statistical simulations is made. Finally, a numerically advantageous discretisation is compared to the standard approach, derived from a discretized action, and regions of lattice spacings with overlapping results are identified.