Boudewijn F. Roukema, Vincent Blanloeil
The approximate homogeneity of spatial sections of the Universe is well
supported observationally, but the inhomogeneity of 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
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. 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
topological evolution occur at post-quantum epochs if the bang time varies by
much more than a Planck time. Both require physics beyond the Einstein
equations. A phenomenological outline for modelling the evolution from a simply
connected spatial section to a multiply connected section is proposed.
View original:
http://arxiv.org/abs/1201.5845
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