Deriving loop quantum cosmology dynamics from diffeomorphism invariance
Deriving loop quantum cosmology dynamics from diffeomorphism invariance
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DOI：
10.1103/physrevd.98.023505
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发表时间：
2018-02
影响因子：
5
通讯作者：
J. Engle;Ilya Vilensky
中科院分区：
文献类型：
--
作者：
J. Engle;Ilya Vilensky
我们利用比安奇I背景下的量子同态不变性的要求来推导量子哈密顿约束的形式。在施加正确的经典行为，并作出一定的极小假设，我们然后得到一个独特的表达式为量子哈密顿算符比安奇我领先的顺序在$\hbar$。具体来说，这个表达式被发现完全匹配的形式提出的Ashtekar和威尔逊-尤因在圈量子宇宙学（LQC）的文献。此外，通过使用投影映射从量子态的比安奇我模型的各向同性模型的状态，我们约束的动力学也在均匀各向同性的情况下，并获得，再次领先的顺序在$\hbar$，一个独特的量子约束，完全匹配的标准“改进的动力学”的Ashtekar，Pawlowski和辛格。我们的研究结果加强了对LQC动力学及其观测预测的信心，因为它们是更基本的基本原理的结果。
We use the requirement of diffeomorphism invariance in the Bianchi I context to derive the form of the quantum Hamiltonian constraint. After imposing the correct classical behavior and making a certain minimality assumption we then obtain a unique expression for the quantum Hamiltonian operator for Bianchi I to leading order in $\hbar$. Specifically, this expression is found to exactly match the form proposed by Ashtekar and Wilson-Ewing in the loop quantum cosmology (LQC) literature. Furthermore, by using the projection map from the quantum states of the Bianchi I model to the states of the isotropic model, we constrain the dynamics also in the homogeneous isotropic case, and obtain, again to leading order in $\hbar$, a unique quantum constraint which exactly match the standard `improved dynamics' of Ashtekar, Pawlowski and Singh. Our results strengthen confidence in LQC dynamics and its observational predictions as consequences of more basic fundamental principles.