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arXiv 0812.0272gr-qc
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关于各向同性圈量子宇宙学中大爆炸奇异性的解决

On the resolution of the big bang singularity in isotropic Loop Quantum Cosmology

Madhavan Varadarajan

摘要:

与以前的工作相比,在没有高阶曲率修正的情况下,我们构造了具有无质量标量场的平坦各向同性模型的圈量子宇宙学(LQC)。约束的物质部分包含逆三元组算子,该算子可以使用或不使用类似于Thiemann的过程来量化。与后者的选择,我们表明,LQC量子化是相同的标准惠勒德维特理论(WDW),其中没有奇异性的决议。我们认为,前者的选择导致奇点决议的意义上的一个定义明确的,定期(向后)的演变,通过和超越的时代,宇宙的大小消失。我们的工作与Ashtekar,Pawlowski和辛格(APS)的开创性工作一起澄清了在奇异性解决方案中的三个“异国情调”结构在这个LQC模型中的作用,即:曲率校正,逆三重定义和“聚合物”性质的运动表示。我们还批判地考察了APS在分析WDW半经典态时所作的某些技术假设,指出了WDW半经典态波函数的红外行为所引起的一些问题

英文摘要:

In contrast to previous work in the field, we construct the Loop Quantum Cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the Hamiltonian constraint. The matter part of the constraint contains the inverse triad operator which can be quantized with or without the use of a Thiemann- like procedure. With the latter choice, we show that the LQC quantization is identical to that of the standard Wheeler DeWitt theory (WDW) wherein there is no singularity resolution. We argue that the former choice leads to singularity resolution in the sense of a well defined, regular (backward) evolution through and beyond the epoch where the size of the universe vanishes. Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three `exotic' structures in this LQC model, namely: curvature corrections, inverse triad definitions and the `polymer' nature of the kinematic representation. We also critically examine certain technical assumptions made by APS in their analysis of WDW semiclassical states and point out some problems stemming from the infrared behaviour of their wave functions

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