Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
复制标题
DOI：
10.1103/physrevd.102.126024
复制
发表时间：
2020-07
影响因子：
5
通讯作者：
K. Giesel;Bao-Fei Li;Parampreet Singh
中科院分区：
文献类型：
--
作者：
K. Giesel;Bao-Fei Li;Parampreet Singh
本文研究了具有Starobinsky暴胀势的空间平坦FLRW模型中高斯尘埃和Brown-Kuchasiness尘埃以及无质量Klein-Gordon标量参考场的圈量子宇宙学（LQC）的约化相空间量子化.这是一个“双流体”模型，其中参考场充当全球时钟，在暴胀时空中提供物理时间，并允许绕过传统量子宇宙学模型中的各种技术障碍。约化相空间是根据引力和暴胀子自由度的狄拉克可观量得到的。这两个尘埃模型的物理汉密尔顿量具有相同的形式，但与克莱因-戈登参考场的物理汉密尔顿量有很大不同，这反映了时间的多项选择问题的一个方面。使用所谓的$\bar \mu$方案实现了圈量子化，得到了包含在尘埃和无质量Klein-Gordon模型中产生物理时间演化的物理哈密顿算符的薛定谔方程.这些原来是量子差分方程具有相同的非奇异结构的LQC中的其他模型。我们研究了一些唯象的量子化的影响，使用有效的动力学产生的减少相空间量子化，包括大爆炸奇异性的分辨率通过量子反弹，和不同的参考场的影响，在这两个前通货膨胀和慢卷通货膨胀阶段的e-折叠。我们发现，不同的时钟，即使从一个小的但相同的能量密度开始，也会在暴胀动力学上留下微小但不同的印记。此外，对于布朗-库恰西尘埃，选择负能量密度会导致在暴胀开始之前的循环演化，从而限制了理想时钟的某些值。
We explore a reduced phase space quantization of loop quantum cosmology (LQC) with Gaussian and Brown-Kuchař dust, and massless Klein-Gordon scalar reference fields for a spatially flat FLRW model with a Starobinsky inflationary potential. This is a ``two-fluid" model in which reference fields act as global clocks providing a physical time in an inflationary spacetime, and allow bypassing various technical hurdles in conventional quantum cosmological models. The reduced phase space is obtained in terms of the Dirac observables of the gravitational as well as the inflaton degrees of freedom. The physical Hamiltonians of the two dust models take the same form but turn out to be quite different from that of the Klein-Gordon reference field which reflects an aspect of the multiple choice problem of time. Loop quantization is implemented using the so-called $\bar \mu$ scheme and the Schrodinger equations involving the physical Hamiltonian operators generating the evolution in the physical time in the dust and massless Klein-Gordon models are obtained. These turn out to be quantum difference equations with same non-singular structure as for other models in LQC. We study some phenomenological implications of the quantization using the effective dynamics resulting from the reduced phase space quantization including the resolution of the big bang singularity via a quantum bounce, and effects of the different reference fields on e-foldings in both the pre-inflation and the slow-roll inflationary phases. We find that different clocks, even when starting with a small but same energy density, can leave tiny but different imprints on the inflationary dynamics. In addition, for Brown-Kuchař dust, the choice of a negative energy density can result in a cyclic evolution before the onset of inflation constraining certain values for ideal clocks.