Towards a Cosmological subsector of Spin Foam Quantum Gravity
arXiv:1704.03691 · doi:10.1103/PhysRevD.96.086009
Abstract
We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model. The state sum is restricted to certain symmetric configurations which resembles the geometry of a flat homogeneous and isotropic universe. The vertex structure is specially chosen so that a basic concept of expansion and contraction of the lattice universe is allowed. We compute the asymptotic form of the spin foam state sum in the symmetry restricted setting, and recover a Regge-type action, as well as an explicit form of the Hessian matrix, which captures quantum corrections. We investigate the action in the three cases of vacuum, a cosmological constant, and coupled to dust, and find that in all cases, the corresponding FRW dynamics is recovered in the limit of large lattices. While this work demonstrates a large intersection with computations done in the context of cosmological modelling with Regge Calculus, it is ultimately a setup for treating curved geometries in the renormalization of the EPRL-FK spin foam model.
arXiv comment38 pages, 10 figures
References in corpus (56)
- The Spin Foam Approach to Quantum Gravity
- LQG vertex with finite Immirzi parameter
- Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
- Relativistic spin networks and quantum gravity
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- Planck stars
- Lorentzian spin foam amplitudes: graphical calculus and asymptotics
- Asymptotic analysis of the EPRL four-simplex amplitude
- On the semiclassical limit of 4d spin foam models
- Towards Spinfoam Cosmology
- Improved and Perfect Actions in Discrete Gravity
- Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
- Spin-Foams for All Loop Quantum Gravity
- Realistic Observable in Background-Free Quantum Gravity: the Planck-Star Tunnelling-Time
- Area-angle variables for general relativity
- Decorated tensor network renormalization for lattice gauge theories and spin foam models
- Numerical evidence for a phase transition in 4d spin foam quantum gravity
- (Broken) Gauge Symmetries and Constraints in Regge Calculus
- From the discrete to the continuous - towards a cylindrically consistent dynamics
- Perfect discretization of reparametrization invariant path integrals
- Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
- The complete LQG propagator: II. Asymptotic behavior of the vertex
- Regge calculus from a new angle
- A note on area variables in Regge calculus
- Holonomy Spin Foam Models: Definition and Coarse Graining
- Path integral measure and triangulation independence in discrete gravity
- Towards a phase diagram for spin foams
- Hypercuboidal renormalization in spin foam quantum gravity
- Time evolution as refining, coarse graining and entangling
- Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
- A new perspective on cosmology in Loop Quantum Gravity
- Quantum Gravity as Topological Quantum Field Theory
- Coarse graining flow of spin foam intertwiners
- A new look at loop quantum gravity
- Coarse graining of spin net models: dynamics of intertwiners
- Quantum group spin nets: refinement limit and relation to spin foams
- In quantum gravity, summing is refining
- Spinfoams in the holomorphic representation
- Discretization independence implies non-locality in 4D discrete quantum gravity
- Renormalization of Discrete Models without Background
- Pachner moves in a 4d Riemannian holomorphic Spin Foam model
- Dirac's discrete hypersurface deformation algebras
- Bubble divergences and gauge symmetries in spin foams
- The Holst Spin Foam Model via Cubulations
- Constraints on Area Variables in Regge Calculus
- A Homogeneous Model of Spinfoam Cosmology
- Variation of Area Variables in Regge Calculus
- Operator Spin Foams: holonomy formulation and coarse graining
- Regge calculus models of closed lattice universes
- Regge calculus models of the closed vacuum -FLRW universe
- A cosmological solution of Regge calculus
- On background-independent renormalization of spin foam models
- On the Schlafli differential formula
- Expanding Polyhedral Universe in Regge Calculus
- Cosmological modelling with Regge calculus
Cited by in corpus (23)
- Effective Spin Foam Models for Lorentzian Quantum Gravity
- SU(2) graph invariants, Regge actions and polytopes
- Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
- Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
- Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
- Primordial fluctuations from quantum gravity
- Emergence of Spacetime in a restricted Spin-foam model
- Searching for classical geometries in spin foam amplitudes: a numerical method
- Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
- Quantum Gravity on the computer: Impressions of a workshop
- On the volume simplicity constraint in the EPRL spin foam model
- Numerical evaluation of spin foam amplitudes beyond simplices
- Lorentzian quantum cosmology from effective spin foams
- Deformation of the EPRL spin foam model by a cosmological constant
- Hamiltonian Renormalisation V: Free Vector Bosons
- Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
- Toward matter dynamics in spin foam quantum gravity
- Curvature effects in the spectral dimension of spin foams
- Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
- A Monte Carlo algorithm for spin foam intertwiners
- Non-convex 4d polytopes in Spin Foam Models
- Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity
- (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality