On the topological implications of inhomogeneity

Details On the topological implications of inhomogeneity On the topological implications of inhomogeneity

2012-01-27

arxiv.org/abs/1201.5845v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

17 pages, 4 figures, submitted to Classical and Quantum Gravity

Scientific paper

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.

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