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We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology.
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Although observational data reinforce flat topologies, closed scenarios provide a qualitative description of flat cases just looking for scales much lower than the size of the radius of S 3 S^{3} . For additional details about the suitability of closed (and/or compact) topologies see, e.g., Ref. [ 24 ]
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