Abstract
The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or “causal sets”. The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity. In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.
Highlights
Causal set theory (CST) refers to the specific proposal made by Bombelli, Lee, Meyer and Sorkin (BLMS) in their 1987 paper (Bombelli et al 1987)
The continuum approximation of causal set theory (CST) is an implementation of a deep result in Lorentzian geometry due to Hawking et al (1976) and its generalisation by Malament (1977), which states that the causal structure determines the conformal geometry of a future and past distinguishing causal spacetime
We describe in brief some of the exciting phenomenology that comes out of the kinematical structure of causal sets. This includes the momentum space diffusion coming from CST discreteness (“swerves”) (Dowker et al 2004) and the effects of non-locality on quantum field theory (Sorkin 2007b), which includes a recent proposal for dark matter (Saravani and Afshordi 2017)
Summary
Causal set theory (CST) refers to the specific proposal made by Bombelli, Lee, Meyer and Sorkin (BLMS) in their 1987 paper (Bombelli et al 1987). A recent analytic calculation in Loomis and Carlip (2018) showed that a subdominant class of non-manifold-like causal sets, the bilayer posets, are suppressed in the path integral when using the BD action, under certain dimension dependent conditions satisfied by the parameter space This gives hope that such an effective dynamics might be able to overcome the entropy of the non-manifold-like causal sets. 7, we describe in brief some of the exciting phenomenology that comes out of the kinematical structure of causal sets This includes the momentum space diffusion coming from CST discreteness (“swerves”) (Dowker et al 2004) and the effects of non-locality on quantum field theory (Sorkin 2007b), which includes a recent proposal for dark matter (Saravani and Afshordi 2017). While the original argument was a kinematic estimate, dynamical models of fluctuating Λ were subsequently examined (Ahmed et al 2004; Ahmed and Sorkin 2013; Zwane et al 2018) and have been compared with recent observations (Zwane et al 2018)
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