Effective Hamiltonian for Isotropic Loop Quantum Cosmology

Details Effective Hamiltonian for Isotropic Loop Quantum Cosmology Effective Hamiltonian for Isotropic Loop Quantum Cosmology

2004-07-19

arxiv.org/abs/gr-qc/0407073v3

Class.Quant.Grav. 21 (2004) 4941-4953

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, revtex4, one figure. In version 2, only e-print archive numbers are corrected. In this final version minor typos are

Scientific paper

10.1088/0264-9381/21/21/012

For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential equation admits a `unique' non-singular continuation through vanishing triad. A WKB approximation for the solutions leads to an effective continuum Hamiltonian. The effective dynamics is also non-singular (no big bang singularity) and approximates the classical dynamics for large volumes. The effective evolution is thus a more reliable model for further phenomenological implications of the small volume effects.

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