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arXiv 2204.07589gr-qc
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圈量子宇宙学及其规范协变化身：弱曲率关系

Loop quantum cosmology and its gauge-covariant avatar: a weak curvature relationship

Bao-Fei Li, Parampreet Singh

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14 pages
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摘要：

我们探讨了标准圈量子宇宙学（LQC）中的有效动力学之间的关系，基于完整性和从规范固定通量获得的三元组，和修改的LQC的基础上完整性和规范协变通量（简称gLQC）。由于非微扰量子几何效应导致能量密度的最大值，这两种模型都通过反弹产生奇异性分辨率。在LQC中，反弹被能量密度中的$ρ^2$项非常好地捕获，该项具有负号，其作为对经典Friedmann和Raychaudhuri方程的非微扰修改而出现。但是，由于规范协变通量修改的艰巨性，gLQC中的这种修改的细节仍然是隐藏的，这不允许以封闭形式写出上述方程。为了提取这些修改，我们探讨了大体积，弱曲率极限的物质与一个固定的状态方程，并获得高阶修正的经典理论。我们发现，在gLQC的弱曲率极限下，在后反弹分支中，超越经典理论的一阶修正完全恢复了LQC的修正Friedmann和Raychaudhuri方程的形式.相比之下，由于gLQC中的非对称反弹，反弹前分支的弱曲率极限呈现出新颖的结构，其中$ρ^{3/2}$项作为超越经典理论的一阶校正，而$ρ^2$项作为二阶校正出现。我们的工作表明，gLQC有一个更丰富的结构，其中包括非微扰修改的LQC在其弱曲率极限的动力学方程的形式。这表明宇宙学扇区的更一般的圈量子化可以在某些截断下揭示LQC，并且可能存在隐藏在LQC设置中的量子几何的潜在有趣的高阶修改。

英文摘要：

We explore the relationship between the effective dynamics in standard loop quantum cosmology (LQC) based on holonomies and triads obtained from gauge-fixing fluxes, and a modification of LQC based on holonomies and gauge-covariant fluxes (referred to as gLQC). Both the models yield singularity resolution via a bounce because of non-perturbative quantum geometric effects resulting in a maximum for energy density. In LQC, the bounce is extremely well captured by a $ρ^2$ term in energy density with a negative sign which emerges as a non-perturbative modification to the classical Friedmann and Raychaudhuri equations. But, details of such modifications in gLQC have remained hidden due to an arduous nature of gauge-covariant flux modifications which do not allow writing above equations in a closed form. To extract these modifications we explore the large volume, weak curvature limit for matter with a fixed equation of state and obtain higher order corrections to the classical theory. We find that in the weak curvature limit of gLQC, in the post-bounce branch, the first order correction beyond classical theory fully recovers the form of modified Friedmann and Raychaudhuri equations of LQC. In contrast, due to an asymmetric bounce in gLQC, the weak curvature limit of the pre-bounce branch exhibits a novel structure with a $ρ^{3/2}$ term as a first order correction beyond classical theory while the $ρ^2$ term appears as a second order correction. Our work shows that gLQC has a far richer structure which includes the form of dynamical equations with non-perturbative modifications in LQC in its weak curvature limit. This indicates that more general loop quantizations of cosmological sectors can reveal LQC at some truncation, and possibly there exist a tower of potentially interesting higher order modifications from quantum geometry which are hidden in the setting of LQC.

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