Observables for cyclic causal set cosmologies

TL;DR

This paper develops new algebraic frameworks for analyzing cyclic cosmological models within causal set theory, focusing on observables related to universe cycles with infinitely many breaks or posts.

Contribution

It introduces two novel algebras of observables for cyclic causal set cosmologies, providing new tools for understanding universe dynamics with infinite cycles.

Findings

Constructed algebra from cylinder sets with single maximal elements

Defined algebra generated by stem-sets with physical interpretation

Established theorems for cyclic dynamics with infinitely many posts

Abstract

In causal set theory, cycles of cosmic expansion and collapse are modelled by causal sets with "breaks" and "posts" and a special role is played by cyclic dynamics in which the universe goes through perpetual cycles. We identify and characterise two algebras of observables for cyclic dynamics in which the causal set universe has infinitely many breaks. The first algebra is constructed from the cylinder sets associated with finite causal sets that have a single maximal element and offers a new framework for defining cyclic dynamics as random walks on a novel tree. The second algebra is generated by a collection of stem-sets and offers a physical interpretation of the observables in these models as statements about unlabeled stems with a single maximal element. There are analogous theorems for cyclic dynamics in which the causal set universe has infinitely many posts.