Towards Spinfoam Cosmology
arXiv:1003.3483 · doi:10.1103/PhysRevD.82.084035
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.
8 pages
References in corpus (20)
- Quantum Nature of the Big Bang: Improved dynamics
- Quantum Nature of the Big Bang
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- Loop quantum cosmology of k=1 FRW models
- The loop-quantum-gravity vertex-amplitude
- Flipped spinfoam vertex and loop gravity
- Loop Quantum Cosmology: An Overview
- The Classical Universes of the No-Boundary Quantum State
- The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
- Is loop quantization in cosmology unique?
- The complete LQG propagator: II. Asymptotic behavior of the vertex
- Stepping out of Homogeneity in Loop Quantum Cosmology
- Effective Constraints for Quantum Systems
- Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
- Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
- Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
- Semiclassical analysis of the Loop Quantum Gravity volume operator: Area Coherent States
Cited by in corpus (13)
- Polyhedra in loop quantum gravity
- Spinning Loop Black Holes
- Cosmological constant in spinfoam cosmology
- Generalized Spinfoams
- A new look at loop quantum gravity
- Dynamics for a 2-vertex Quantum Gravity Model
- Spinfoams in the holomorphic representation
- Local spinfoam expansion in loop quantum cosmology
- Vertex Expansion for the Bianchi I model
- Coherent states for FLRW space-times in loop quantum gravity
- On the structure of a background independent quantum theory: Hamilton function, transition amplitudes, classical limit and continuous limit
- Big Bounce in Dipole Cosmology
- Quantum cosmology for the 21st century: A debate