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density of matter. Nonetheless the argument that the mean density of matter in the real world was smaller than the best vacuum we could obtain in laboratories on Earth, in other words that we could treat de Sitter’s model as a close approximation to reality, was a dodge. And scientists knew it. After all, theoretical zero density is not the same as a very small density.
    But the paradox was soon resolved. The Russian mathematician and meteorologist Aleksandr Aleksandrovich Friedman published two papers presenting his discovery of a whole class of spatially homogeneous and isotropic solutions to Einstein’s equations of which Einstein’s and de Sitter’s solutions were special cases. 11 In this class there was only one static model (Einstein’s); all the others were either expanding or shrinking. He also explained the apparently paradoxical status of de Sitter’s solution: all the models expanding out to infinity (monotonically) tended to de Sitter’s empty model as time tended to plus infinity. Thus de Sitter’s state was effectively an asymptotic state for the expanding models, in which the density of matter tended to zero in outcome of the expansion.
    Gradually the situation was starting to clear up. Einstein’s proposition that there was only one unique, uniquely possible cosmological model concordant with all the philosophical expectations turned out not to hold. In cosmology, as in all the other branches of physics, many models can be constructed and only observation will tell which of them corresponds best to the reality in the world.
    Cosmology would not become a fully experimental science until the last decades of the twentieth century, but it started to mature already by the 1920s. In 1929 Edwin Hubble collated about 40 results for the red shift measurements in the spectra of galaxies and published his famous law: the velocity at which a galaxy is moving away is directly proportional to its distance from us. 12 These results were already in circulation among scientists. In 1927 Georges Lemaître compared the results of measurements of the red shift with predictions for one of the solutions discovered by Friedman, which he had found independently of Friedman, and confirmed that there was no discrepancy between the theory and observations. 13
    In the 1930s the paradigm of an expanding universe became firmly established. Even Einstein, who for a long time would not accept it, finally had to concede in the face of facts. The reason for his opposition had been that an expanding universe suggested the idea that it must have had a beginning. Knowing the distance to a few galaxies and the velocities at which they were receding, on the basis of Hubble’s law it is easy to estimate how long ago all the galaxies were situated “at one point.” For Einstein this was a difficult conclusion to accept. A universe which was supposed to be self-explanatory should not have a beginning.

Michael Heller, Ultimate Explanations of the Universe , DOI: 10.1007/978-3-642-02103-9_3, © Springer-Verlag Berlin Heidelberg 2009
    3. A Cyclical Universe
    Michael Heller 1 
(1) 
ul. Powstańców Warszawy 13/94, 33-110 Tarnów, Poland

Michael  Heller
Email: [email protected]

    Abstract
    By about the mid-1920s it was evident that an eternal universe could not be kept on in relativistic cosmology “at a low cost.” Not only does Einstein’s static model contradict observations and experimentally measured values for the red shift in galactic spectra, but – as Eddington showed – it is also unstable: it cannot persist in a state of “static equilibrium,” and the occurrence of even a slight perturbation, which is what gravitation does by its very nature, would give rise either to its collapse or expansion. Thus all the indications are that the universe is not static but dynamic. But a dynamic universe implies the question of a beginning. The first measurements of the red shift suggested, and Hubble’s subsequent work