Spatial Hypersurfaces in Causal Set Cosmology

Abstract

Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an antichain. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by an inextendible antichain. We construct a richer structure corresponding to a thickening of this antichain containing non-trivial geometric and topological information. We find that covariant observables can be associated with such thickened antichains and transitions between them, in classical stochastic growth models of causal sets. This construction highlights the difference between the covariant measure on causal set cosmology and the standard sum-over-histories approach: the measure is assigned to completed histories rather than to histories on a restricted spacetime region. The resulting re-phrasing of the sum-over-histories may be fruitful in other approaches to quantum gravity.

Revtex, 12 pages, 2 figures

References in corpus (3)

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• A general solution for classical sequential growth dynamics of Causal Sets
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Cited by in corpus (9)

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• On Recovering Continuum Topology from a Causal Set
• Spacelike distance from discrete causal order
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• Algebraic Classical and Quantum Field Theory on Causal Sets
• Steps towards Lorentzian quantum gravity with causal sets
• The structure of covtree: searching for manifestly covariant causal set dynamics
• Inference of Boundaries in Causal Sets
• Black holes and singularities in causal set gravity