Stepping out of Homogeneity in Loop Quantum Cosmology

Abstract

We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation.

16 pages

References in corpus (36)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• LQG vertex with finite Immirzi parameter
• Spin Foam Models for Quantum Gravity
• Loop Quantum Cosmology
• Weaving a classical geometry with quantum threads
• A new spinfoam vertex for quantum gravity
• Dark Energy from structure: a status report
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Isotropic Loop Quantum Cosmology
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Flipped spinfoam vertex and loop gravity
• The physical hamiltonian in nonperturbative quantum gravity
• Graviton propagator from background-independent quantum gravity
• The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
• Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Quantum Theory of Geometry III: Non-commutativity of Riemannian Structures
• Loop quantum cosmology and inhomogeneities
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Quantum tetrahedra and simplicial spin networks
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Particle scattering in loop quantum gravity
• The semiclassical approximation to quantum gravity
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Group Integral Techniques for the Spinfoam Graviton Propagator
• Lorentzian LQG vertex amplitude
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• Towards the graviton from spinfoams: higher order corrections in the 3d toy model
• Towards the graviton from spinfoams: the 3d toy model
• Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
• A semiclassical tetrahedron

Cited by in corpus (68)

• Loop Quantum Cosmology: A Status Report
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• The Spin Foam Approach to Quantum Gravity
• Loop quantum cosmology of Bianchi type IX models
• Towards Spinfoam Cosmology
• Phase space descriptions for simplicial 4d geometries
• Gauge-Invariant Perturbations in Hybrid Quantum Cosmology
• The universe as a quantum gravity condensate
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Exotic singularities and spatially curved Loop Quantum Cosmology
• From the discrete to the continuous - towards a cylindrically consistent dynamics
• On the geometry of loop quantum gravity on a graph
• Observational issues in loop quantum cosmology
• Quantum-Reduced Loop Gravity: Cosmology
• Casting Loop Quantum Cosmology in the Spin Foam Paradigm
• Cosmic recall and the scattering picture of Loop Quantum Cosmology
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Consistent Loop Quantum Cosmology
• Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion
• From covariant to canonical formulations of discrete gravity
• A new perspective on cosmology in Loop Quantum Gravity
• Cosmological constant in spinfoam cosmology
• A new look at loop quantum gravity
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Quantum Reduced Loop Gravity: Semiclassical limit
• Dynamics for a 2-vertex Quantum Gravity Model
• Group field theory condensate cosmology: An appetizer
• A proposed proper EPRL vertex amplitude
• Singularity avoidance in quantum-inspired inhomogeneous dust collapse
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• Complex Ashtekar variables and reality conditions for Holst's action
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
• Local spinfoam expansion in loop quantum cosmology
• Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
• Classical Setting and Effective Dynamics for Spinfoam Cosmology
• Backreaction in Cosmology
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• Quantum-Reduced Loop-Gravity: Relation with the Full Theory
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• The perturbed universe in the deformed algebra approach of Loop Quantum Cosmology
• Group theoretical Quantization of Isotropic Loop Cosmology
• Primordial fluctuations from quantum gravity
• On the spinfoam expansion in cosmology
• Spinfoam Cosmology: quantum cosmology from the full theory
• Symmetry Reduction of Loop Quantum Gravity
• The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity
• On the Expansions in Spin Foam Cosmology
• Vertex Expansion for the Bianchi I model
• Learning about Quantum Gravity with a Couple of Nodes
• 2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
• How to detect an anti-spacetime
• Quantum simulations of a qubit of space
• Embedding loop quantum cosmology without piecewise linearity
• Coherent states for FLRW space-times in loop quantum gravity
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
• Relational Quantum Cosmology
• Quantum theory of electromagnetic fields in a cosmological quantum spacetime
• One vertex spin-foams with the Dipole Cosmology boundary
• Big Bounce in Dipole Cosmology
• How many quanta are there in a quantum spacetime?
• Classical dynamics for Loop Gravity: The 2-vertex model
• Second-order amplitudes in loop quantum gravity
• Spin foams
• From loop quantum gravity to cosmology: the two-vertex model
• Taming Thiemann's Hamiltonian constraint in canonical loop quantum gravity: reversibility, eigenstates and graph-change analysis
• U(N) invariant dynamics for a simplified Loop Quantum Gravity model
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects