Spinfoam cosmology with the proper vertex amplitude

TL;DR

This paper applies the proper vertex amplitude in spinfoam cosmology to derive a transition amplitude resembling the Hartle-Hawking wavefunction, showing it satisfies a Hamiltonian constraint and dynamically selects relevant states.

Contribution

It introduces the use of the proper vertex amplitude in cosmological calculations, ensuring correct semi-classical behaviour and dynamic state selection.

Findings

The amplitude satisfies the Hamiltonian constraint of FRW cosmology.

The proper vertex amplitude leads to correct semi-classical limits.

Dynamical selection influences long-range correlations.

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.