Fluctuations and Correlations in Causal Set Theory

TL;DR

This paper analyzes statistical fluctuations in causal set theory, especially focusing on the causal set action, and introduces tools to account for correlations, aiding future investigations of discreteness effects in quantum gravity models.

Contribution

It develops a decomposition method for fluctuations of the causal set action that accounts for correlations, applicable to causal sets approximated by any spacetime.

Findings

Decomposition of fluctuations into correlation-dependent contributions

Tools for calculating fluctuations in causal set quantities

Framework applicable to any spacetime manifold approximation

Abstract

We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal intervals with different cardinalities. We present a convenient decomposition of the fluctuations of the causal set action into contributions that depend on different kinds of correlations. This decomposition can be used in causal sets approximated by any spacetime manifold $\mathcal M$. Our work paves the way for investigating a number of interesting discreteness effects, such as certain aspects of the Everpresent $\Lambda$ cosmological model.