Coherent states for FLRW space-times in loop quantum gravity

Details Coherent states for FLRW space-times in loop quantum gravity Coherent states for FLRW space-times in loop quantum gravity

2010-11-25

arxiv.org/abs/1011.5676v2

Phys.Rev.D83:044029,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 1 figure, published version

Scientific paper

10.1103/PhysRevD.83.044029

We construct a class of coherent spin-network states that capture proprieties of curved space-times of the Friedmann-Lama\^itre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial ($t=$const.) section with dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex $SL(2, \mathbbm{C})$ variables, one for each link of the graph and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in Spin Foams.

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