Curved space equilibration versus flat space thermalization: A short review

We discuss equilibration process in expanding universes as compared to the thermalization Minkowski space--time. The final goal is answer following question: Is equilibrium reached before rapid expansion stops and quantum effects have a negligible effect on background geometry or stress--energy fluxes highly curved early Universe strong rate only after drastic decrease of space--time curvature? argue that consideration more generic non--invariant states theories with invariant actions necessary ingredient understand field dynamics strongly backgrounds. are talking about such which correlation functions not isometry invariants geodesic distances, while having correct UV behaviour. reason consider presence IR secular memory for time dependent backgrounds, totally absent equilibrium. These affect destiny observables space--times.