标题： 无冻结的宇宙学演化与非单调内部时钟 显示英文标题

标题： Freeze-free cosmological evolution with a non-monotonic internal clock

摘要： 由于广义相对论系统中缺乏绝对时间参数，量子宇宙学通常通过两个自由度之间的关系变化来描述宇宙的膨胀，例如物质和几何结构。 然而，如果时钟自由度（自）相互作用非平凡，它们通常会有转折点，在这些转折点上它们的动量为零。 在转折点及其之后，其他自由度的演化不再直接由时钟参数的变化来描述，因为时钟停止后又开始反向运动，而时间则继续向前。 先前尝试以具有转折点的时钟为基础描述量子演化的方法失败了，导致冻结演化，即自由度保持不变，而时钟参数被直接解释为单调时间的替代品，并被推过其转折点。 在此，一种之前在振荡器系统中使用的新方法被应用于一个可处理的宇宙学模型，该模型由具有空间曲率和标量物质的各向同性宇宙组成。 重新坍缩的尺度因子是一个具有单个转折点的时钟示例。 该方法通过解开时钟的转折点，引入了一个与非单调时钟自由度相关但不相同的有效单调时间参数，成功地定义了幺正且无冻结的演化。 基于解析和数值计算，在转折点附近发现了新的量子特征。 显示英文摘要

摘要： Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry. However, if clock degrees of freedom (self-)interact non-trivially, they in general have turning points where their momenta vanish. At and beyond a turning point, the evolution of other degrees of freedom is no longer described directly by changes of the clock parameter because it stops and then turns back, while time is moving forward. Previous attempts to describe quantum evolution relative to a clock with turning points have failed and led to frozen evolution in which degrees of freedom remain constant while the clock parameter, interpreted directly as a substitute for monotonic time, is being pushed beyond its turning point. Here, a new method previously used in oscillator systems is applied to a tractable cosmological model, given by an isotropic universe with spatial curvature and scalar matter. The re-collapsing scale factor presents an example of a clock with a single turning point. The method succeeds in defining unitary and freeze-free evolution by unwinding the turning point of the clock, introducing an effective monotonic time parameter that is related to but not identical with the non-monotonic clock degree of freedom. Characteristic new quantum features are found around the turning point, based on analytical and numerical calculations.