2010/03/17 by Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto · 1 citation
Physics and Astronomy · #gr-qc #astro-ph.CO #hep-th
paper · pdf · doi:10.1103/physrevd.82.084035
published as Phys.Rev.D82:084035,2010 · 8 pages
arxiv created 2010/03/17 · arxiv updated 2010/10/27
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.