Article Title

Spatial hypersurfaces in causal set cosmology

Type of Work

Article

Date

2006

Journal Title

Classical and Quantum Gravity

Journal ISSN

0264-9381

Journal Volume

23

Journal Issue

14

First Page

4743

Last Page

4752

DOI

10.1088/0264-9381/23/14/011

Abstract

Within the causal set approach to quantum gravity, a discrete analogue 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 sequential 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.

Hamilton Areas of Study

Physics