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

中文翻译：

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弯曲空间平衡与平面空间热化：简短回顾

我们讨论了膨胀宇宙中的平衡过程与闵可夫斯基时空中的热化过程。最终目标是回答以下问题：在快速膨胀停止之前达到平衡，量子效应对背景几何的影响可以忽略不计，还是高度弯曲的早期宇宙中的应力-能量通量对膨胀率和只有在时空曲率急剧下降后才能达到平衡？我们认为，在具有不变作用的理论中考虑更通用的非不变状态是理解强弯曲背景中的量子场动力学的必要因素。我们正在讨论这样的状态，其中相关函数不是等距不变量（如测地距离）的函数，同时具有正确的 UV 行为。考虑这种状态的原因是对于一般的时间相关背景存在 IR 长期记忆效应，这些效应在平衡中完全不存在。这些效应强烈影响高度弯曲时空中可观测物体的命运。