Consistent probabilities in loop quantum cosmology
Consistent probabilities in loop quantum cosmology
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DOI：
10.1088/0264-9381/30/20/205008
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发表时间：
2013-10-21
影响因子：
3.5
通讯作者：
Singh, Parampreet
中科院分区：
文献类型：
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作者：
Craig, David A.;Singh, Parampreet
任何量子宇宙学理论的一个基本问题是指定如何将概率分配给各种量子事件或事件序列，例如奇点或反弹的发生。在之前的工作中，我们已经演示了如何在惠勒-德威特量子化宇宙学模型的量子理论的一致历史方法中成功解决这个问题。在这项工作中，我们将这种分析推广到空间平坦、均匀和各向同性宇宙学的精确可解环量化，该宇宙学源自无质量、最小耦合标量场（称为 sLQC）。我们为该模型提供了明确、严格且完整的退相干历史公式，并计算了量子反弹与奇点发生的概率。使用标量场作为涌现的内部时间，我们证明对于一般状态，该模型中奇点发生的概率为零，并且反弹的概率为1，补充了该理论中体积和物质密度期望值的早期研究。我们还从一致的历史观点表明，该模型中的所有状态，无论是量子状态还是经典状态，都在无限“过去”或“未来”标量“时间”的极限内实现了任意大的体积，从某种意义上说，在任意固定体积值下计算的波函数在该极限内消失。最后，我们简要讨论有关一致历史方法在这些模型中的实用性的某些误解。
A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler-DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent-histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce versus a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite 'past' or 'future' scalar 'time', in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models.