Classical Setting and Effective Dynamics for Spinfoam Cosmology

Abstract

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.

38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasized

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Cited by in corpus (21)

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• Introduction to Loop Quantum Cosmology
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective
• Group field theory condensate cosmology: An appetizer
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• Holonomy Operator and Quantization Ambiguities on Spinor Space
• Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
• Duality between Spin networks and the 2D Ising model
• Lorentzian quantum cosmology goes simplicial
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• Spinors and Twistors in Loop Gravity and Spin Foams
• Spinfoams: Foundations
• Classical dynamics for Loop Gravity: The 2-vertex model
• Intertwiner Entanglement Excitation and Holonomy Operator
• From loop quantum gravity to cosmology: the two-vertex model
• New tools for Loop Quantum Gravity with applications to a simple model