Planck 2013 results. XXVI. Background geometry and topology of the Universe

[Timm]

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1. Introduction ...
Thus, the global nature of the Universe we live in is still an open question and studying the observational effects of a possi-ble finite universe is one way to address it.

7. Discussion ...
Depending on the shape of the fundamental domain, we findRi>∼χrec (Table 2) with detailed 99 % confidence limits (con-sidering the likelihood marginalized over the orientation of thefundamental domain) varying from 0.9χrec for the cubic torus ina flat universe to 1.03χrec for the dodecahedron in a positivelycurved universe, with somewhat weaker constraints for poorly-proportioned spaces that are considerably larger along some di-rections