k = 1圈量子宇宙学中量子不确定性的含义：不同的量子反转和超普朗克机制
Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
摘要：
圈量子宇宙学中的空间封闭Friedmann-Lemaitre-Robertson-Walker模型允许两种不等价的相容量子化：一种是基于用封闭圈上的完整性表示场强，另一种是使用连接算子和开放完整性。使用有效动力学，我们调查的两个量子化的单流体和两个流体的情况下，各种状态方程，包括幻影物质的唯象差异。我们发现，两个量子化之间的一个显着差异是存在两个不同的量子翻转，反弹或tumblapses，在连接量子化，在一个单一的独特的量子反弹或tumblapses在holonomy量子化。这些结果推广了Corichi和Karami关于刚性物质存在两个不同量子反弹的早期结果。然而，我们发现，在某些情况下，两个不同的量子反转可以变得几乎无法区分。根据初始条件，一个纯量子循环宇宙也可以存在，经历量子反弹和量子跃迁。我们表明，对于各种状态方程，基于连接的量子化导致超普朗克值的能量密度和膨胀标量在量子转折。有趣的是，我们发现，非常极端的能量密度也可以发生的holonomy量子化，突破了空间平坦的圈量子化模型中的最大允许密度。然而，在所有这些情况下，扩展标量都由一个普适值限制。
英文摘要：
The spatially closed Friedmann-Lemaître-Robertson-Walker model in loop quantum cosmology admits two inequivalent consistent quantizations: one based on expressing the field strength in terms of the holonomies over closed loops, and, another using a connection operator and open holonomies. Using the effective dynamics, we investigate the phenomenological differences between the two quantizations for the single fluid and the two fluid scenarios with various equations of state, including the phantom matter. We show that a striking difference between the two quantizations is the existence of two distinct quantum turnarounds, either bounces or recollapses, in the connection quantization, in contrast to a single distinct quantum bounce or a recollapse in the holonomy quantization. These results generalize an earlier result on the existence of two distinct quantum bounces for stiff matter by Corichi and Karami. However, we find that in certain situations two distinct quantum turnarounds can become virtually indistinguishable. And depending on the initial conditions, a pure quantum cyclic universe can also exist undergoing a quantum bounce and a quantum recollapse. We show that for various equations of states, connection based quantization leads to super-Planckian values of the energy density and the expansion scalar at quantum turnarounds. Interestingly, we find that very extreme energy densities can also occur for the holonomy quantization, breaching the maximum allowed density in the spatially flat loop quantized model. However, the expansion scalar in all these cases is bounded by a universal value.
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