论文标题
循环量子宇宙学及其量规化的化身：弱曲率关系
Loop quantum cosmology and its gauge-covariant avatar: a weak curvature relationship
论文作者
论文摘要
我们探讨了基于固体和固定量磁通量获得的标准环量子宇宙学（LQC）（LQC）中的有效动力学之间的关系，以及基于载体的LQC和衡量量的Fluxes（称为GLQC）的LQC的修改。由于非扰动量子几何影响，这两个模型都通过反弹产生奇异性分辨率，从而最大值能量密度。在LQC中，弹跳被能量密度的$ρ^2 $项所捕获，其负符号是对经典Friedmann和Raychaudhuri方程的非扰动修饰。但是，由于仪表量化的通量修改的艰巨性质，GLQC中这种修改的细节仍然隐藏了，这些变化不允许以封闭形式的方程式上方写入方程式。为了提取这些修改，我们探索了较大的体积，具有固定状态方程式物质的弱曲率极限，并获得了经典理论的更高级校正。我们发现，在BLQC的弱曲率限制中，在弹跳后分支中，超出经典理论的一阶校正完全恢复了LQC修改的Friedmann和Raychaudhuri方程的形式。相比之下，由于GLQC中的不对称弹跳，反弹前分支的弱曲率极限表现出具有$ρ^{3/2} $项的新型结构，作为一阶校正，而不是经典理论，而$ρ^2 $术语则作为二阶校正。我们的工作表明，GLQC具有更丰富的结构，其中包括在LQC中以其弱曲率极限的LQC进行非扰动修饰的动力学方程形式。这表明，宇宙学部门的更一般的循环量化可以在某些截断下揭示LQC，并且可能存在一个潜在的有趣的高阶塔塔塔，而量子几何形状则隐藏在LQC的环境中。
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.
