A general property of universes without initial singularity is investigated
based on the singularity theorem, assuming the null convergence condition and
the global hyperbolicity. As a direct consequence of the singularity theorem,
the universal covering of a Cauchy surface of a nonsingular universe with a
past trapped surface must have the topology of $S^3$. In addition, we find that
the affine size of a nonsingular universe, defined through the affine length of
null geodesics, is bounded above. In the case where a part of the nonsingular
spacetime is described by Friedmann-Lema\^itre-Robertson-Walker spacetime, we
find that this upper bound can be understood as the affine size of the
corresponding closed de Sitter universe. We also evaluate the upper bound of
the affine size of our Universe based on the trapped surface confirmed by
recent observations of baryon acoustic oscillations, assuming that our Universe
has no initial singularity.



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