Directions in Causal Set Quantum Gravity

TL;DR

This paper reviews the development of causal set quantum gravity, highlighting recent progress such as a causal set expression for the Einstein-Hilbert action and a scalar field propagator, while outlining future research directions.

Contribution

It provides a comprehensive overview of causal set theory, emphasizing recent advances and identifying future research directions in quantum gravity.

Findings

Development of a causal set expression for the Einstein-Hilbert action

Construction of a scalar field Feynman propagator on a causal set

Broad overview of progress and future directions in causal set quantum gravity

Abstract

In the causal set approach to quantum gravity the spacetime continuum arises as an approximation to a fundamentally discrete substructure, the causal set, which is a locally finite partially ordered set. The causal set paradigm was elucidated in a classic paper by Bombelli, Lee, Meyer and Sorkin in 1987. While early kinematical results already showed promise, the program received a substantial impetus about a decade ago with the work of Rideout and Sorkin on a classical stochastic growth dynamics for causal sets. Considerable progress has been made ever since in our understanding of causal set theory while leaving undisturbed the basic paradigm. Recent highlights include a causal set expression for the Einstein-Hilbert action and the construction of a scalar field Feynman propagator on a fixed causal set. The aim of the present article is to give a broad overview of the results in causal set theory while pointing out directions for future investigations.