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**cyclic model**is any of several cosmological models in which the universe follows infinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.

## Contents |

## Overview

In the 1930s, theoretical physicists, most notably Albert Einstein, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. However, work by Richard C. Tolman in 1934 showed that these early attempts failed because of the entropy problem that, in statistical mechanics, entropy only increases because of the Second law of thermodynamics.^{[1]}This implies that successive cycles grow longer and larger. Extrapolating back in time, cycles before the present one become shorter and smaller culminating again in a Big Bang and thus not replacing it. This puzzling situation remained for many decades until the early 21st century when the recently discovered dark energy component provided new hope for a consistent cyclic cosmology.

^{[2]}

One new cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. It was proposed in 2001 by Paul Steinhardt of Princeton University and Neil Turok of Cambridge University. The theory describes a universe exploding into existence not just once, but repeatedly over time.

^{[3]}

^{[4]}The theory could potentially explain why a mysterious repulsive form of energy known as the "cosmological constant", and which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard Big Bang model.

A different cyclic model relying on the notion of phantom energy was proposed in 2007 by Lauris Baum and Paul Frampton of the University of North Carolina at Chapel Hill.

^{[5]}

## The Steinhardt–Turok model

In this cyclic model, two parallel orbifold planes or M-branes collide periodically in a higher dimensional space.^{[6]}The visible four-dimensional universe lies on one of these branes. The collisions correspond to a reversal from contraction to expansion, or a big crunch followed immediately by a big bang. The matter and radiation we see today were generated during the most recent collision in a pattern dictated by quantum fluctuations created before the branes. Eventually, the universe reached the state we observe today, before beginning to contract again many billions of years in the future. Dark energy corresponds to a force between the branes, and serves the crucial role of solving the monopole, horizon, and flatness problems. Moreover the cycles can continue indefinitely into the past and the future, and the solution is an attractor, so it can provide a complete history of the universe.

As Richard C. Tolman showed, the earlier cyclic model failed because the universe would undergo inevitable thermodynamic heat death.

^{[1]}However, the newer cyclic model evades this by having a net expansion each cycle, preventing entropy from building up. However, there are major problems with the model. Foremost among them is that colliding branes are not understood by string theorists, and nobody knows if the scale invariant spectrum will be destroyed by the big crunch. Moreover, like cosmic inflation, while the general character of the forces (in the ekpyrotic scenario, a force between branes) required to create the vacuum fluctuations is known, there is no candidate from particle physics.

^{[7]}

## The Baum–Frampton model

This more recent cyclic model of 2007 makes a different technical assumption concerning the equation of state of the dark energy which relates pressure and density through a parameter**w**.

^{[5]}

^{[8]}It assumes

**w**< -1 (a condition called phantom energy) throughout a cycle, including at present. (By contrast, Steinhardt-Turok assume

**w**is never less than -1.) In the Baum-Frampton model, a septillionth (or less) of a second before the would-be Big Rip, a turnaround occurs and only one causal patch is retained as our universe. The generic patch contains no quark, lepton or force carrier; only dark energy - and its entropy thereby vanishes. The adiabatic process of contraction of this much smaller universe takes place with constant vanishing entropy and with no matter including no black holes which disintegrated before turnaround. The idea that the universe "comes back empty" is a central new idea of this cyclic model, and avoids many difficulties confronting matter in a contracting phase such as excessive structure formation, proliferation and expansion of black holes, as well as going through phase transitions such as those of QCD and electroweak symmetry restoration. Any of these would tend strongly to produce an unwanted premature bounce, simply to avoid violation of the second law of thermodynamics. The surprising

**w**< -1 condition may be logically inevitable in a truly infinitely cyclic cosmology because of the entropy problem. Nevertheless, many technical back up calculations are necessary to confirm consistency of the approach. Although the model borrows ideas from string theory, it is not necessarily committed to strings, or to higher dimensions, yet such speculative devices may provide the most expeditious methods to investigate the internal consistency. The value of

**w**in the Baum-Frampton model can be made arbitrarily close to, but must be less than, -1.

## Notes

- ^
^{a}^{b}R.C. Tolman (1987) [1934].*Relativity, Thermodynamics, and Cosmology*. New York: Dover. LCCN 34032023-{{{3}}}. ISBN 0486653838. **^**P.H. Frampton (2006). "On Cyclic Universes".*arΧiv:astro-ph/0612243*[astro-ph].**^**P.J. Steinhardt, N. Turok (2001). "Cosmic Evolution in a Cyclic Universe".*arΧiv:hep-th/0111098*[hep-th].**^**P.J. Steinhardt, N. Turok (2001). "A Cyclic Model of the Universe".*arΧiv:hep-th/0111030*[hep-th].- ^
^{a}^{b}L. Baum, P.H. Frampton (2007). "Entropy of Contracting Universe in Cyclic Cosmology".*arΧiv:hep-th/0703162*[hep-th]. **^**P.J. Steinhardt, N. Turok (2004). "The Cyclic Model Simplified".*arΧiv:astro-ph/0404480*[astro-ph].**^**P. Woit (2006).*Not Even Wrong*. London: Random House. ISBN 97800994488644.**^**L. Baum and P.H. Frampton (2007). "Turnaround in Cyclic Cosmology".*Physical Review Letters***98**(7): 071301. doi:10.1103/PhysRevLett.98.071301. arXiv:hep-th/0610213. PMID 17359014.

## See also

## Further reading

- P.J. Steinhardt, N. Turok (2007).
*Endless Universe*. New York: Doubleday. ISBN 9780385509640. - R.C. Tolman (1987) [1934].
*Relativity, Thermodynamics, and Cosmology*. New York: Dover. LCCN 34032023-{{{3}}}. ISBN 0486653838. - L. Baum and P.H. Frampton (2007). "Turnaround in Cyclic Cosmology".
*Physical Review Letters***98**(7): 071301. doi:10.1103/PhysRevLett.98.071301. arXiv:hep-th/0610213. PMID 17359014. - R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson, "Cosmic Black-Body Radiation,"
*Astrophysical Journal***142**(1965), 414. This paper discussed the oscillatory universe as one of the main cosmological possibilities of the time. - S. W. Hawking and G. F. R. Ellis,
*The large-scale structure of space-time*(Cambridge, 1973).

## External links

- Paul J. Steinhardt, Department of Physics, Princeton University
- Paul H. Frampton, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill
- Cyclic universe on arxiv.org
- "The Cyclic Universe": A Talk with Neil Turok
- Roger Penrose - Cyclical Universe Model

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