"Observables" in causal set cosmology

TL;DR

This paper explores how to define and interpret covariant observables in causal set cosmology, proposing a characterization of measurable covariant sets in terms of stem sets within classical sequential growth models.

Contribution

It introduces a meaningful way to identify covariant measurable collections of causal sets, addressing the challenge of covariance in quantum gravity models.

Findings

Characterization of covariant measurable sets as unions and differences of stem sets

Clarification of the role of transition probabilities in classical sequential growth dynamics

Insight into the interpretation of covariant observables in quantum gravity

Abstract

The ``generic'' family of classical sequential growth dynamics for causal sets provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum theory. In particular we can investigate how general covariance manifests itself and address the problem of identifying and interpreting covariant ``observables'' in quantum gravity. The problem becomes, in this setting, that of identifying measurable covariant collections of causal sets, to each of which corresponds the question: ``Does the causal set that occurs belong to this collection?'' It has for answer the probability measure of the collection. Answerable covariant questions, then, correspond to measurable collections of causal sets which are independent of the labelings of the causal sets. However, what the transition probabilities of the classical sequential growth dynamics provide directly is a measure on the space of {\it labeled} causal sets and the physical interpretation of the covariant measurable collections is consequently obscured. We show that there is a physically meaningful characterisation of the class of measurable covariant sets as unions and differences of ``stem sets''.