Towards a cosmological subsector of spin foam quantum gravity
Towards a cosmological subsector of spin foam quantum gravity
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DOI：
10.1103/physrevd.96.086009
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发表时间：
2017-04
影响因子：
5
通讯作者：
Benjamin Bahr;Sebastian Kloser;G. Rabuffo
中科院分区：
文献类型：
--
作者：
Benjamin Bahr;Sebastian Kloser;G. Rabuffo
本文在EPRL-FK自旋泡沫模型的背景下研究了欧氏量子引力的四维路径积分。状态和被限制到某些对称的配置，类似于一个平坦的均匀和各向同性的宇宙的几何形状。顶点结构是经过特殊选择的，以便允许晶格宇宙膨胀和收缩的基本概念。我们计算的自旋泡沫态和的对称性限制设置的渐近形式，并恢复一个雷吉型的行动，以及明确的形式的海森矩阵，它捕获量子校正。我们调查的行动在真空，宇宙常数，并耦合到尘埃的三种情况下，发现在所有情况下，相应的FRW动力学恢复在大晶格的限制。虽然这项工作证明了一个大的交叉点，在宇宙学建模与Regge演算的背景下完成的计算，它最终是一个设置处理弯曲的几何形状在重整化的EPRL-FK自旋泡沫模型。
We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model. The state sum is restricted to certain symmetric configurations which resembles the geometry of a flat homogeneous and isotropic universe. The vertex structure is specially chosen so that a basic concept of expansion and contraction of the lattice universe is allowed. We compute the asymptotic form of the spin foam state sum in the symmetry restricted setting, and recover a Regge-type action, as well as an explicit form of the Hessian matrix, which captures quantum corrections. We investigate the action in the three cases of vacuum, a cosmological constant, and coupled to dust, and find that in all cases, the corresponding FRW dynamics is recovered in the limit of large lattices. While this work demonstrates a large intersection with computations done in the context of cosmological modelling with Regge Calculus, it is ultimately a setup for treating curved geometries in the renormalization of the EPRL-FK spin foam model.