A typical geometry extracted from the path integral of a quantum theory of gravity may be quite complicated in the UV region. Even if a single configuration is not physical, its properties may be of interest to understand the details of its nature, since some universal features can be important for the physics of the model. If the formalism describing the geometry is coordinate independent, which is the case in the model studied here, such understanding may be facilitated by the use of suitable coordinate systems. In this article we use scalar fields that solve Laplace’s equation to introduce coordinates on geometries with a toroidal topology. Using these coordinates we observe what we identify as the cosmic voids and filaments structure, even if matter is only a tool to visualize the geometry. We also show that if the scalar fields we used as coordinates are dynamically coupled to geometry, they can change it in a dramatic way, leading to a modification of the spatial topology.

从量子引力理论的路径积分中提取的典型几何形状在紫外线区域可能非常复杂。即使单个配置不是物理配置，其属性也可能有助于了解其性质的细节，因为某些通用特征对于模型的物理特性可能很重要。如果描述几何的形式主义是独立于坐标的，这里研究的模型就是这种情况，则可以通过使用合适的坐标系来促进这种理解。在本文中，我们使用解拉普拉斯方程的标量场来引入具有环形拓扑结构的几何体的坐标。使用这些坐标，我们观察到我们所识别的宇宙空隙和细丝结构，即使物质只是一种可视化几何的工具。