Topological implications of inhomogeneity
  The approximate homogeneity of spatial sections of the Universe is well
supported observationally, but the inhomogeneity of the spatial sections is
even better supported. Here, we consider the implications of inhomogeneity in
dust models for the connectedness of spatial sections at early times. We
consider a non-global Lemaitre-Tolman-Bondi (LTB) model designed to match
observations, a more general, heuristic model motivated by the former, and two
specific, global LTB models. We propose that the generic class of solutions of
the Einstein equations projected back in time from the spatial section at the
present epoch includes subclasses in which the spatial section evolves (with
increasing time) smoothly (i) from being disconnected to being connected, or
(ii) from being simply connected to being multiply connected, where the
coordinate system is comoving and synchronous. We show that (i) and (ii) each
contain at least one exact solution. These subclasses exist because the
Einstein equations allow non-simultaneous big bang times. The two types of
topology evolution occur over time slices that include significantly
post-quantum epochs if the bang time varies by much more than a Planck time. In
this sense, it is possible for cosmic topology evolution to be "mostly"
classical.
