Quantum field thermalization in expanding backgrounds

The 2PI effective action formalism for quantum fields out of equilibrium is set up in an expanding (Friedmann-Robertson-Walker) background. We write down and solve the evolution equations for a φ4 model at O(λ2) in a coupling expansion. We comment on issues of renormalization, lattice discretization and the range of applicability of the approach. A number of example calculations are presented, including thermalization and (p)reheating. Generalizations to more complicated systems and applications are discussed.