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The loop quantization of the negatively curved k=-1 RW model poses severaltechnical challenges. We show that the issues can be overcome and a successfulquantization is possible that extends the results of the k=0,+1 models in anatural fashion. We discuss the resulting dynamics and show that for a universeconsisting of a massless scalar field, a bounce is predicted in the backwardevolution in accordance with the results of the k=0,+1 models. We also showthat the model predicts a vacuum repulsion in the high curvature regime thatwould lead to a bounce even for matter with vanishing energy density. Wefinally comment on the inverse volume modifications of loop quantum cosmologyand show that, as in the k=0 model, the modifications depend sensitively on theintroduction of a length scale which a priori is independent of the curvaturescale or a matter energy scale.Comment: Clarified some of the discussion and updated reference

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Loop quantum cosmology and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math>Robertson-Walker model

Loop quantum cosmology and thek=−1Robertson-Walker model