Effective Hamiltonian for Isotropic Loop Quantum Cosmology

Abstract

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.

18 pages, revtex4, one figure. In version 2, only e-print archive numbers are corrected. In this final version minor typos are corrected and an extra para of explanation added in the discussion. To appear in Class. Quantum Grav