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Some Cosmological Models

Mogens True Wegener
Year: 2002 Pages: 9
Revised version (20.12.2008).

Accepting clock retardation as an empirical fact, we provisionally adopt Whitrow's derivation of the Robertson-Walker Metric (RWM) of Cosmology from the gamma-factor of SR. Recalling the fact that the principle of cosmic isotropy can be used as an argument for the definability of an all-embracing universal time, at least statistically, we propose to reverse this procedure by postulating such time as a regulative idea in the sense of Kant. Taking RWM as our formal point of departure we next investigate the properties of two standard models of modern cosmology: !) the uniform expansion model of Milne & Prokhovnik, which is the simplest model of a cosmic "big bang", and 2) the exponential expansion model of Bondi & Gold, supposed to be the simplest model of a cosmic "steady state". Rejecting the so-called "perfect cosmological principle" of the latter, it is easy to show that the ideas of "big bang" and "steady state" may not be mutually exclusive after all: a universe starting with a "big bang" at the dawn of creation may approximate to a "steady state" in the course of infinite time. We further consider the relationship between our choice of time scale for a particular model of the universe and its corresponding space metric. As it turns out, there are at least two important ways of mapping the expansion of the universe: a) that which keeps atomic sizes constant while light is being stretched, and b) that which keeps distances between fundamental particles constant while their constituents are shrinking. Finally a new model of the universe is proposed which deviates from RWM by allowing the curvature of space to vary with distance. In this model the curvature of space appears to increase with the distance at which an object is observed by a fundamental observer. The model suggested is a new "steady state" model which is even simpler than that of Bondi & Gold in the sense that it implies an absolute structural identity between "world map" and "world view", in agreement with the "no-horizon" principle of Milne. The basic properties of this model and two other related ones are examined and discussed.