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arXiv · 1611.01508

Spinfoam cosmology with the proper vertex amplitude

Ilya Vilensky
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Abstract

The proper vertex amplitude is derived from the EPRL vertex by restricting to a single gravitational sector in order to achieve the correct semi-classical behaviour. We apply the proper vertex to calculate a cosmological transition amplitude that can be viewed as the Hartle-Hawking wavefunction. To perform this calculation we deduce the integral form of the proper vertex and use extended stationary phase methods to estimate the large-volume limit. We show that the resulting amplitude satisfies an operator constraint whose classical analogue is the Hamiltonian constraint of the Friedmann-Robertson-Walker cosmology. We find that the constraint dynamically selects the relevant family of coherent states and demonstrate a similar dynamic selection in standard quantum mechanics. We investigate the effects of dynamical selection on long-range correlations.

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Ilya Vilensky. 2017-03-29. Spinfoam cosmology with the proper vertex amplitude. https://doi.org/10.1088/1361-6382%2Faa91f4

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