Compact hyperbolic universe and singularities

Details Compact hyperbolic universe and singularities Compact hyperbolic universe and singularities

1996-05-18

arxiv.org/abs/gr-qc/9605041v1

Phys.Rev. D54 (1996) 7303-7310

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages with 7 figures

Scientific paper

10.1103/PhysRevD.54.7303

Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices. Though the universal covering space of the universe has a past Cauchy horizon and can be extended analytically beyond it, the extended region has densely many points which correspond to singularities of the compact universe. The result is essentially attributed to the ergodicity of the geodesic flow on a compact negatively curved manifold. Validity of the result is also discussed in the case of inhomogeneous universe. Relationship with the strong cosmic censorship conjecture is also discussed.

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