Oscillatory universe

The oscillatory universe is a cosmological model, originally derived by Alexander Friedman in 1922, investigated briefly by Einstein in 1930 and critiqued by Richard Tolman in 1934, in which the universe undergoes a series of oscillations, each beginning with a big bang and ending with a big crunch. After the big bang, the universe expands for a while before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.

Scientific Issues

In the simple cases studied by Friedman [cite journal | author = Friedman, A. | title = Über die Krümmung des Raumes | journal = Z. Phys. | volume = 10 | year = 1922| pages = 377–386 | doi = 10.1007/BF01332580 (English translation in: Gen. Rel. Grav. 31 (1999), 1991-2000.)] , containing just homogeneous matter and possibly a negative cosmological constant, each "bounce" is a gravitational singularity with infinite density and zero size. It is then a matter of taste whether to extend the solution through the singularities, giving an infinitely oscillating model, or to assume that only one cycle exists. The oscillating model was once popular among cosmologists who thought that the singularities could be avoided and so each big bang would be connected to an earlier big crunch: the mathematical singularities seen in calculations were supposed to be the result of over-idealizations (e.g. assuming too much symmetry or neglecting some force), and would be resolved by a more careful treatment, or by an alternative theory of gravity such as Brans-Dicke theory. In this case, as pointed out by Tolman [cite book | author= Tolman, R. C.| title= Relativity, Thermodynamics, and Cosmology | location=Oxford | publisher=Clarendon Press | year=1934 | id=LCCN 340-32023 Reissued (1987) New York: Dover ISBN 0-486-65383-8.] , entropy would build up from oscillation to oscillation; according to Tolman this would cause each oscillation to last longer and reach a larger size than the one before, in some sense tending towards a condition of heat death. However, in the 1960s, Stephen Hawking, Roger Penrose and George Ellis showed that singularities were a universal feature of cosmologies with a big bang and that no feature of general relativity could prevent them. Since no "memory" of previous cycles would be preserved, the entropy issue was eliminated, but by the same token there was little reason to postulate cycles before or after the present one. Other measurements suggested the universe is not closed. These arguments caused most cosmologists to abandon the oscillating universe model.

John Archibald Wheeler, who believed that a closed universe was necessary on general principles, speculated that the fundamental physical constants could be re-processed to new values at each bounce, providing a mechanism for anthropic selection. [cite book | author = Misner, C. W., Thorne, K. S., Wheeler, J. A. | year = 1973 |title = Gravitation | chapter = §44.6 | publisher = Freeman | location = New York | isbn = 0-7167-0344-0 (This section based on a lecture by Wheeler).] [Wheeler, J. A. (1977) in "Foundational problems in the special sciences", Reidel, Dordrecht, pp 3–33]

The theory has been revived in brane cosmology as the cyclic model, which evades most of the arguments leveled against the oscillatory universe in the sixties. Despite some success, the theory is still controversial, largely because there is no satisfactory string theoretic description of the bounce in this model.


  • R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson, "Cosmic Black-Body Radiation," "Astrophysical Journal" 142 (1965), 414. This important paper discusses the oscillatory universe as one of the main cosmological possibilities.
    # S. W. Hawking and G. F. R. Ellis, "The large-scale structure of space-time" (Cambridge, 1973).

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