arXiv 1111.17662011-11-07gr-qchep-th

圈量子宇宙学从圈量子引力的产生：h中的最低阶

Emergence of Loop Quantum Cosmology from Loop Quantum Gravity: Lowest Order in h

Chun-Yen Lin

备注：: 31 pages MikteX file with 1 pdf figure
发表信息：: Chin. J. Phys. 53 (2015) 110104
DOI：: 10.6122/CJP.20150911

摘要：

为了从圈量子引力导出圈量子宇宙学，我将\cite{lin1}中给出的模型应用于引力场和物质场耦合的系统。物质扇区由充当宇宙时钟的标量场$phi$和提供物理空间坐标和框架的其他场${psi}$组成。从圈量子引力的运动学希尔伯特空间出发，构造了该模型的物理希尔伯特空间，并利用物质坐标和标架构造了物理希尔伯特空间中的定域观测量。然后选择一个特定的相干物理状态，其局部可观测量的期望值在晚时钟时间产生均匀、各向同性和空间平坦的引力场和$phi$场。控制这些场的方程可以利用物理希尔伯特空间的对称性导出。当${psi}$的物质反作用可以忽略时，结果给出了一个特殊的$O(hbar^0)$近似的圈量子宇宙模型，并给出了可计算的高阶修正。

英文摘要：

To derive loop quantum cosmology from loop quantum gravity, I apply the model given in \cite{lin1} to a system with coupled gravitational and matter fields. The matter sector consists of a scalar field $phi$ serving as a cosmological clock, and other fields ${psi}$ providing physical spatial coordinates and frames. The physical Hilbert space of the model is constructed from the kinematical Hilbert space of loop quantum gravity, and the local observables in the physical Hilbert space are constructed using the matter coordinates and frames. A specific coherent physical state is then chosen, whose expectation values of the local observables give rise to homogeneous, isotropic and spatially flat gravitational and $phi$ fields at a late clock time. The equations governing these fields may be derived using the symmetry of the physical Hilbert space. When the matter back reactions from ${psi}$ are negligible, the result gives a specific loop quantum cosmological model in the $O(hbar^0)$ approximation, with calculable higher order corrections.

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英文摘要：

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