Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 8 (2012), 001, 26 pages      arXiv:1110.0646      http://dx.doi.org/10.3842/SIGMA.2012.001
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Numerical Techniques in Loop Quantum Cosmology

David Brizuela a, Daniel Cartin b and Gaurav Khanna c
a) Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA
b) Naval Academy Preparatory School, 197 Elliot Avenue, Newport, Rhode Island 02841, USA
c) Physics Department, University of Massachusetts at Dartmouth, North Dartmouth, Massachusetts 02747, USA

Received October 01, 2011, in final form December 20, 2011; Published online January 02, 2012

Abstract
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues.

Key words: quantum gravity; numerical techniques; loop quantum cosmology.

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