Cosmological Constant in LQG Vertex Amplitude

Details Cosmological Constant in LQG Vertex Amplitude Cosmological Constant in LQG Vertex Amplitude

2011-05-11

arxiv.org/abs/1105.2212v2

Phys. Rev. D 84, 064010 (2011)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, 5 figures, result and presentation improved

Scientific paper

10.1103/PhysRevD.84.064010

A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity) embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.

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