The structure of covtree: searching for manifestly covariant causal set dynamics

TL;DR

This paper investigates the structure of covtree, a covariant framework for causal set dynamics, identifying special paths and their relation to physical properties, and introduces a transformation akin to cosmic renormalization.

Contribution

It analyzes covtree's structure, characterizes paths related to physical features, and proposes a transformation for covtree dynamics similar to known renormalization methods.

Findings

Covtree has a self-similar structure.

Identified paths corresponding to posts and breaks.

Derived a transformation similar to cosmic renormalization.

Abstract

Covtree - a partial order on certain sets of finite, unlabeled causal sets - is a manifestly covariant framework for causal set dynamics. Here, as a first step in picking out a class of physically well-motivated covtree dynamics, we study the structure of covtree and the relationship between its paths and their corresponding infinite unlabeled causal sets. We identify the paths which correspond to posts and breaks, prove that covtree has a self-similar structure, and write down a transformation between covtree dynamics akin to the cosmic renormalisation of Rideout and Sorkin's Classical Sequential Growth models. We identify the paths which correspond to causal sets which have a unique natural labeling, thereby solving for the class of dynamics which give rise to these causal sets with unit probability.