Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989ap%26ss.158....1g&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 158, no. 1, Aug. 1989, p. 1-7.
Astronomy and Astrophysics
Astrophysics
1
Astronomical Models, Big Bang Cosmology, Universe, Distance, Horizon, Luminosity
Scientific paper
The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2 x pi squared x R cubed (t), instead of pi squared x R cubed (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, the maximum volume exists at any cosmic time t in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the time of the maximum scale factor. The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as is should be. This leads to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.
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