Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
复制标题
聚合物和 GUP 扩展范式中 Bianchi I 宇宙学的半经典和量子动力学比较
DOI：
--
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
G. Montani
中科院分区：
文献类型：
--
作者：
G. Barca;E. Giovannetti;G. Montani
我们详细比较了聚合物量子力学和广义不确定性原理方法，以阐明我们可以在多大程度上以同样的基础对待它们。我们证明，虽然在半经典层面上它们可以被表述为泊松代数的类似修改，但在量子层面上它们本质上是不同的，因为 PQM 并不意味着位置上的绝对最小不确定性。然后，我们在半经典水平上将这些方案应用于 Bianchi I 宇宙学，仅对宇宙体积的代数进行变形，寻找能够解释膜宇宙学和环量子宇宙学中出现的修正弗里德曼方程的替代公式。在纯量子层面上，我们通过原始设置实现了这两种方法，并将所得的两个惠勒-德威特方程简化为相同的形态结构，展示了聚合物形式主义如何与弹跳动力学相关，而在广义不确定性原理情况下奇点仍然存在。两种方法还讨论了波包传播的含义，概述了当奇点存在时，普朗克时代必然会通过宇宙的完全量子（非峰值）状态来接近。
We compare in some detail Polymer Quantum Mechanics and the Generalized Uncer- tainty Principle approach to clarify to what extent we can treat them on the same footing. We show that, while on a semiclassical level they may be formulated as similar modifications of the Poisson algebra, on a quantum level they intrinsically differ because PQM implies no absolute minimal uncertainty on position. Then we implement these schemes to Bianchi I cosmology on a semiclassical level de-forming only the algebra of the Universe volume, searching for alternative formulations able to account for the modified Friedmann equations emerging in Brane Cosmology and Loop Quantum Cosmology. On a pure quantum level, we implement the two approaches through their original se-tups and reduce the two resulting Wheeler-DeWitt equations to the same morphological structure, showing how the polymer formalism is associated with a bouncing dynamics while in the Generalized Uncertainty Principle case the singularity is still present. The implications of the wavepacket spreading are also discussed in both approaches, outlining that, when the singularity survives, the Planckian era must necessarily be approached by a fully quantum (non-peaked) state of the Universe.