A **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.

## 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

## 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