Mathematics – Logic
Scientific paper
Sep 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974rspsa.340..263j&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 340, Issue 1622, pp. 263-286
Mathematics
Logic
2
Scientific paper
An autonomous system of equations, describing uniform cosmological models, is formulated by using the perfect fluid approximation of Einstein's equations. These equations contain an arbitrary function related to the matter content of the universe, which may include negative energy fields. This function, designated α , is assumed to depend on the density and expansion rate of the universe only. Geometrical methods of analysis are used to study the behaviour of all models described by this system. The analysis shows that there are only three possible modes of behaviour that can be exhibited by a uniform universe. Examples of the first two classes are well known in the 'big-bang' and 'steady-state' theories. However, it is shown that the familiar theories are not unique, but an infinite number of both such types of model exist for various α . It is also shown that all steady-state models in an expanding universe are stable. The third class of model, associated with periodic behaviour, is of two types. The first is demonstrated by a universe which oscillates between expansion and contraction but never achieves infinite density. The second consists of ever-expanding (or contracting) models in which the density and expansion rate oscillate between finite values. These latter models possess evolutionary characteristics on 'short' time-scales, while satisfying the 'perfect cosmological principle' in the large, and only arise in the presence of gross non-linearities introduced by the function α . Both the periodic and steady-state classes occur only in the case of negative energy fields.
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