Asymptotic Properties of Difference Equations for Isotropic Loop Quantum 
Cosmology

Bojowald, Martin; Rej, Adam

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Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology

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Bojowald, Martin
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Bojowald, M., & Rej, A. (2005). Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology. Classical Quantum Gravity, 22, 3399-3420.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4F28-A

Abstract

In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general properties of solutions can appear differently. Properties of particular interest are boundedness and the presence of small-scale oscillations. Continued fraction techniques are used to show in different matter models the presence of special initial conditions leading to bounded solutions, and an explicit expression for these initial values is derived.