Cosmological constant from condensation of defect excitations

TL;DR

This paper constructs quantum gravity states in 2+1 dimensions from defect excitations that model different cosmological constants, providing a unified framework for describing homogeneous geometries and potential applications in quantum cosmology and condensed matter.

Contribution

It introduces a novel family of quantum gravity states based on defect excitations that encode various cosmological constants within a unified Hilbert space framework.

Findings

States describe homogeneously curved geometries on large scales

States form an anomaly-free algebra for different cosmological constants

Construction extends to 4D with string-like defects and Crane-Yetter model

Abstract

A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of $(2+1)$-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.