Closed universe - Their future evolution and final state

Details Closed universe - Their future evolution and final state Closed universe - Their future evolution and final state

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985mnras.216..395b&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 216, Sept. 15, 1985, p. 395-402.

Mathematics

36

Cosmology, Hypergeometric Functions, Singularity (Mathematics), Space-Time Functions, Topology, Universe, Astronomical Models, Cauchy Problem, Existence Theorems, Quantum Theory

Scientific paper

The authors summarize what is currently known about the future evolution and final state of closed universes: in mathematical language, those which have a compact Cauchy surface. It is shown that the existence of a maximal hypersurface (a time of maximum expansion) is a necessary and sufficient condition for the existence of an all-encompassing final singularity in a universe with a compact Cauchy surface. The only topologies which can admit maximal hypersurfaces are S3 and S2×S1, together with more complicated topologies formed from these two types of 3-manifold by connected summation and certain identifications. The relevance of these results to inflation is also discussed.

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