Coherent states for FLRW space-times in loop quantum gravity

TL;DR

This paper develops a new class of coherent spin-network states in loop quantum gravity that model curved FLRW space-times, bridging quantum states with classical cosmological geometries.

Contribution

It introduces a novel construction of coherent states peaked on FLRW geometries using complex SL(2,C) variables, applicable to both Euclidean and Lorentzian signatures.

Findings

Reproduces flat space semiclassical states in Euclidean limit

Constructs states for curved FLRW space-times

Applicable to both Euclidean and Lorentzian signatures

Abstract

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.