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arXiv · 1003.3483

Towards Spinfoam Cosmology

Eugenio Bianchi·Carlo Rovelli·Francesca Vidotto
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Abstract

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.

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Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto. 2010-03-17. Towards Spinfoam Cosmology. https://doi.org/10.1103/physrevd.82.084035

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