Generating function techniques for loop quantum cosmology

Abstract

Loop quantum cosmology leads to a difference equation for the wave function of a universe, which in general has solutions changing rapidly even when the volume changes only slightly. For a semiclassical regime such small-scale oscillations must be suppressed, by choosing the parameters of the solution appropriately. For anisotropic models this is not possible to do numerically by trial and error; instead, it is shown here for the Bianchi I LRS model how this can be done analytically, using generating function techniques. Those techniques can also be applied to more complicated models, and the results gained allow conclusions about initial value problems for other systems.

22 pages, 5 figures; version to appear in CQG

References in corpus (12)

• Background Independent Quantum Gravity: A Status Report
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• Quantum Spin Dynamics (QSD)
• Isotropic Loop Quantum Cosmology
• Homogeneous Loop Quantum Cosmology
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• Isotropic Loop Quantum Cosmology with Matter
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• Comments on the kinematical structure of loop quantum cosmology

Cited by in corpus (25)

• Loop Quantum Cosmology
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Loop Quantum Gravity and the Cyclic Universe
• Numerical loop quantum cosmology: an overview
• Absence of pre-classical solutions in Bianchi I loop quantum cosmology
• Wave functions for the Schwarschild black hole interior
• Coordinate time dependence in Quantum Gravity
• The Volume Operator in Spherically Symmetric Quantum Geometry
• Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
• Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
• Numerical solutions to lattice-refined models in loop quantum cosmology
• Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology
• Numerical Techniques in Loop Quantum Cosmology
• Instabilities in numerical loop quantum cosmology
• The volume operator for spin networks with planar or cylindrical symmetry
• Separable sequences in Bianchi I loop quantum cosmology
• Quantum Geometry and its Implications for Black Holes
• Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology
• Approximate pre-classical solutions in loop quantum cosmology
• Universe scenarios from loop quantum cosmology
• The volume operator for singly polarized gravity waves with planar or cylindrical symmetry
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains
• On the Green's function and iterative solutions of Loop Quantum Cosmology
• Conserved quantities in isotropic loop quantum cosmology