Abstract
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.
Highlights
Lattice approaches based on the path integral formalism constitute an important tool with which one can investigate non-perturbative aspects of many quantum field theories
As regards the more interesting and more complicated four-dimensional Causal Dynamical Triangulations (CDT) model, we have recently analyzed systems with massless scalar fields coupled to the geometry [10], and we have studied point particles
The remaining part of the article is organized as follows: in Section 2 we outline the CDT approach to quantum gravity; in Section 3 we discuss how classical scalar fields can be used to define coordinates in fixed simplicial geometries, and how they in turn help better to understand the geometric structures observed in CDT triangulations; in Section 4 we describe how the classical scalar fields can serve as a tool to define alternative proper-time foliations of the CDT manifolds; in Section 5 we analyze the impact of dynamical scalar fields with non-trivial boundary conditions
Summary
Lattice approaches based on the path integral formalism constitute an important tool with which one can investigate non-perturbative aspects of many quantum field theories. The remaining part of the article is organized as follows: in Section 2 we outline the CDT approach to quantum gravity; in Section 3 we discuss how classical scalar fields can be used to define coordinates in fixed simplicial geometries, and how they in turn help better to understand the geometric structures observed in CDT triangulations; in Section 4 we describe how the classical scalar fields can serve as a tool to define alternative proper-time foliations of the CDT manifolds; in Section 5 we analyze the impact of dynamical scalar fields with non-trivial boundary conditions
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