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Observations indicate that the universe is effectively flat, but they do notrule out a closed universe. The role of positive curvature is negligible atlate times, but can be crucial in the early universe. In particular, positivecurvature allows for cosmologies that originate as Einstein static universes,and then inflate and later reheat to a hot big bang era. These cosmologies haveno singularity, no "beginning of time", and no horizon problem. If the initialradius is chosen to be above the Planck scale, then they also have no quantumgravity era, and are described by classical general relativity throughout theirhistory.Comment: minor changes; version to appear in Class Q Gra

The emergent universe: inflationary cosmology with no singularity