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We investigate (4+1)- and (5+0)-dimensional gravity coupled to a non-compact scalar field sigma-model and a perfect fluid within the context of the Randall-Sundrum scenario. We find cosmological solutions with a rolling fifth radius and a family of warp factors. Included in this family are both the original Randall-Sundrum solution and the self-tuning solution of Kachru, Schulz and Silverstein. Our solutions exhibit conventional cosmology.

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