Mathematics – Logic
Scientific paper
Nov 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ncimb.108.1253t&link_type=abstract
Nuovo Cimento B, Vol. 108, No. 11, p. 1253 - 1273
Mathematics
Logic
6
Universe: Pulsations, Universe: Expansion
Scientific paper
The flatness problem posed by Dicke is studied within the framework of the pulsating model. It is found that Ω is a U-shaped function of the epoch: Ω = ∞ at the bounce as well as at the recollapse point, and has a minimum, which may be close to but exceeding unity, that occurs after the expansion rate a has reached a maximum. The values of Ω, the deceleration parameter, the Hubble constant, and the look-back time for several key values of the expansion epoch are given in closed form. In constrast with the standard model, for q = 1/2, one has Ω > 1. It is proposed that the reason why the universe is apparently near the Ω-minimum at an epoch at which terrestrial science has developed to a point it can make such a determination is because there are relations between the parameters governing the cosmological-expansion and terrestrial-evolution rates, which generate this synchronism. There are two appendices: the first shows in detail that there is no particle horizon problem for the pulsating universe, and the second presents a space-time imbedding argument which clarifies how the expansion rate can exceed the numerical speed of light because it is analogous to a Minkowski proper velocity.
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