Spatial Hypersurfaces in Causal Set Cosmology

Details Spatial Hypersurfaces in Causal Set Cosmology Spatial Hypersurfaces in Causal Set Cosmology

2005-06-29

arxiv.org/abs/gr-qc/0506133v2

Class.Quant.Grav. 23 (2006) 4743-4752

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 12 pages, 2 figures

Scientific paper

10.1088/0264-9381/23/14/011

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.

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