Many-nodes/many-links spinfoam: the homogeneous and isotropic case

Abstract

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large j limit.

8 pages, 4 figures

References in corpus (34)

• Quantum Nature of the Big Bang: Improved dynamics
• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Towards Spinfoam Cosmology
• Is loop quantization in cosmology unique?
• Spinor Representation for Loop Quantum Gravity
• Zakopane lectures on loop gravity
• Stepping out of Homogeneity in Loop Quantum Cosmology
• U(N) tools for Loop Quantum Gravity: The Return of the Spinor
• Path Integrals and the WKB approximation in Loop Quantum Cosmology
• Lorentzian spinfoam propagator
• Operator Spin Foam Models
• Cosmological constant in spinfoam cosmology
• Regularization and finiteness of the Lorentzian LQG vertices
• Dynamics for a 2-vertex Quantum Gravity Model
• Spinfoams in the holomorphic representation
• Regge gravity from spinfoams
• Local spinfoam expansion in loop quantum cosmology
• Simple model for quantum general relativity from loop quantum gravity
• Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
• Spinfoam Cosmology: quantum cosmology from the full theory
• On the Expansions in Spin Foam Cosmology
• Vertex Expansion for the Bianchi I model
• Loop gravity in terms of spinors
• Learning about Quantum Gravity with a Couple of Nodes
• Curvature in spinfoams
• Two-point functions in (loop) quantum cosmology
• Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations
• Coherent states for FLRW space-times in loop quantum gravity
• Big Bounce in Dipole Cosmology
• Discretizing parametrized systems: the magic of Ditt-invariance

Cited by in corpus (28)

• Introduction to Loop Quantum Cosmology
• Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
• Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Group field theory condensate cosmology: An appetizer
• A proposed proper EPRL vertex amplitude
• Primordial fluctuations from quantum gravity
• Searching for classical geometries in spin foam amplitudes: a numerical method
• Learning about Quantum Gravity with a Couple of Nodes
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• Embedding loop quantum cosmology without piecewise linearity
• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Anisotropic Spinfoam Cosmology
• Relational Quantum Cosmology
• Lorentzian quantum cosmology from effective spin foams
• One vertex spin-foams with the Dipole Cosmology boundary
• Spinfoams: Foundations
• Spinfoam cosmology with the proper vertex amplitude
• First-order quantum-gravitational correction to Friedmannian cosmology from covariant, holomorphic spinfoam cosmology
• Tunneling of quantum geometries in spinfoams
• Spin foams
• A note on the spinor construction of Spin Foam amplitudes
• Decoherent Histories of Spin Networks
• Aspects of quantum gravity
• Spinfoam tunneling of quantum geometries in angle variables
• On the dynamics of single-vertex states in quantum-reduced loop gravity
• Asymptotic of Lorentzian Polyhedra Propagator
• Infinities as a measure of our ignorance