Scalar fields in Causal Dynamical Triangulations

TL;DR

This paper explores the use of scalar fields solving Laplace's equation as coordinate systems in quantum gravity geometries, revealing universal structures and dramatic geometric changes when coupled dynamically.

Contribution

It introduces a coordinate system based on scalar fields in quantum gravity geometries and demonstrates their impact on observed structures and geometry evolution.

Findings

Identification of cosmic voids and filaments in quantum geometries

Scalar fields as coordinates reveal universal geometric features

Dynamic coupling of scalar fields significantly alters geometry

Abstract

A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it 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, 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 denote as the "cosmic voids and filaments" structure, even if no matter is present in the theory. 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.