Spinfoam cosmology with the proper vertex amplitude

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.

improved presentation, added references, included discussion of long-range correlations

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• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
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Cited by in corpus (3)

• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Spinfoams: Foundations
• The Chern-Simons Current in Time Series of Knots and Links in Proteins