Cosmological observations in a closed universe

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Abstract
We investigate how a closed Friedmann-Robertson-Walker universe would appear to astronomers living at different cosmic epochs. For this purpose we apply the three observational tests of classical cosmology to closed universe models without a cosmological constant, both for the expanding and for the contracting phases of their evolution. In particular, we investigate how the Hubble diagram and other plots of observational quantities, such as angular size and number density of galaxies, change with cosmic time. Once recollapse has started, these diagrams become multivalued for certain ranges of the observational variables. Light from nearby galaxies is blueshifted whereas galaxies further away have redshifted spectra, these two regions of the observable universe being separated by a 'surface of zero redshift'. In a contracting universe two different images of the same galaxy may appear in opposite directions of the sky since observers can, in principle, see beyond their own antipoles. Because of this and the fact that the cosmological diagrams are multivalued, interpretation of cosmological data could be considerably more difficult in the contracting phase than during the expanding phase of the evolution.

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