含尘渐近DeSitter宇宙诞生的正则变换和隧穿几率
A canonical transformation and the tunneling probability for the birth of an asymptotically DeSitter universe with dust
摘要：
本文研究了具有正宇宙学常数和一般理想流体的封闭Friedmann-Robertson-Walker模型的量子宇宙学描述。我们采用Schutz变分形式。如果使用比例因子和其正则共轭动量作为描述这些模型的几何扇区的相空间变量，则得到具有算子排序模糊性的Wheeler-DeWitt方程。为了避免这些模糊性和简化量子处理的模型，我们引入了新的相空间变量。我们明确证明了从旧变量集到新变量集的转换是规范的。为了证明上述正则变换简化了这些模型的量子处理，我们考虑一个理想流体是尘埃的特定模型。我们用Crank-Nicholson格式数值求解Wheeler-DeWitt方程，并确定初始波函数的时间演化。最后，我们将本模型的结果与另一个模型的结果进行比较，其中唯一的区别是存在辐射完美流体，而不是尘埃。
英文摘要：
In the present work, we study the quantum cosmology description of closed Friedmann-Robertson-Walker models in the presence of a positive cosmological constant and a generic perfect fluid. We work in the Schutz's variational formalism. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we introduce new phase space variables. We explicitly demonstrate that the transformation leading from the old set of variables to the new one is canonical. In order to show that the above canonical transformations simplify the quantum treatment of those models, we consider a particular model where the perfect fluid is dust. We solve the Wheeler-DeWitt equation numerically using the Crank-Nicholson scheme and determine the time evolution of the initial wave function. Finally, we compare the results for the present model with the ones for another model where the only difference is the presence of a radiative perfect fluid, instead of dust.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
