The oscillatory universe is a cosmological model, originally derived by Alexander Friedman in 1922 and developed by Richard Tolman from 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. Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Alexander Alexandrovich Friedman (June 16, 1888 – September 16, Russian cosmologist and mathematician. ... Richard C. Tolman was California Institute of Technology professor of physical chemistry and mathematical physics. ... For other uses, see Big Bang (disambiguation). ... This article is about the cosmological theory. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... This article does not cite any references or sources. ...

Scientific Issues

In the simple cases studied by Friedman^[1], 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 amongst 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^[2], 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. Look up Homogeneous in Wiktionary, the free dictionary. ... In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ... This article or section is in need of attention from an expert on the subject. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... The heat death is a possible final state of the universe, in which it has reached maximum entropy. ... The 1960s decade refers to the years from January 1, 1960 to December 31, 1969, inclusive. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... George Ellis is the Distinguished Professor of Complex Systems at the University of Cape Town (South Africa), in the Department of Mathematics and Applied Mathematics. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ...

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.^[3][4] John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ... In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers. ... In physics and cosmology, the anthropic principle is an umbrella term for various dissimilar attempts to explain the structure of the universe by way of coincidentally balanced features that are necessary and relevant to the existence of observers (usually assumed to be carbon-based life or even specifically human beings). ...

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. Brane cosmology is a protoscience motivated by, but not rigorously derived from, superstring theory and M-theory. ... The cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point...

References

1. ^ Friedman, A. (1922). "Über die Krümmung des Raumes". Z. Phys. 10: 377-386.  (English translation in: Gen. Rel. Grav. 31 (1999), 1991-2000.)
2. ^ Tolman, R. C. (1934). Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. LCCN 340-32023.  Reissued (1987) New York: Dover ISBN 0-486-65383-8.
3. ^ Misner, C. W., Thorne, K. S., Wheeler, J. A. (1973). "§44.6", Gravitation. New York: Freeman. ISBN 0-7167-0344-0.  (This section based on a lecture by Wheeler).
4. ^ Wheeler, J. A. (1977) in Foundational problems in the special sciences, Reidel, Dordrecht, pp 3–33

• 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).