Non-equilibrium quantum phenomena in the early universe

Abstract

We develop and apply to physical problems non-equilibrium quantum field theory techniques. With the mathematical framework provided by the 2PI effective action formalism we write down quantum transport equations for spatially homogeneous and isotropic systems, including coherence effects. The equations are based on the coherent quasiparticle approximation (cQPA), which predicts that quantum coherence effects are condensed on a singular shell at <i>k</i>₀ = 0 in the phase space of the system. We verify the existence of this shell by constructing the two-point function of the fermionic system exactly for a specific time-dependent mass profile, and give a comprehensive analysis of the phase space structures. We also use the exact solution to study the range of validity of the semiclassical approximation, finding out that its range of applicability may be much larger than what is suggested by naïve estimates. We derive simple moment equations for scalar systems in which the loop interactions in the 2PI expansion are local. The equations are then used to study the coupled evolution of one- and two-point functions in two different setups. First, we study the Mexican hat -potential as a representative of a phase transition. Using the Hartree approximation in the 2PI loop expansion, we identify the processes of spinodal decomposition and parametric resonance in the time evolution of the coupled system. We discuss the processes in detail, finding out for example that the spinodal effects can allow the one-point function to cross a classically forbidden potential barrier. The second setup considers a non-minimally coupled spectator field during reheating after inflation. Similarly to the other system we establish the existence of spinodal and parametric effects, this time induced by the oscillating Ricci scalar. We compare the results to those obtained earlier with adiabatic methods, finding out that the non-equilibrium quantum effects can dramatically change the particle production efficiency. Our results emphasize the important and intricate role quantum effects play in non-equilibrium systems. The accurate description of phenomena such as baryogenesis, early universe phase transitions in general and (p)reheating demands for field theoretic techniques capable of treating these non-equilibrium effects properly. Out methods provide new techniques to tackle this challenging task.