A Cyclic Universe

/ by Paul Steinhardt /

Does the universe repeat once every trillion years?

Illustration by The Barbarian Group

How did the universe begin? Did it have a beginning at all? These questions may have been the subject of speculation and debate for millennia, but they have not been widely discussed for the past forty years. Ever since the discovery of the cosmic background radiation in 1965, the overwhelmingly predominant view has been that our universe began about 14 billion years ago in a cosmic fireball known as the “big bang” and that it has been expanding, cooling, and evolving ever since. Recently, though, a small but growing number of theorists have begun to challenge this conventional belief and to pursue a radical new history of the universe. According to this new idea, there was a big bang, but this was not the beginning of space and time. In fact, in the version proposed by Neil Turok and myself, the big bang has occurred myriad times in our universe’s past, repeating at regular intervals during which galaxies, stars, planets, and life form anew. The result is a “cyclic universe” in which cycles extend far into the past and into the future—and perhaps forever.

A challenge to the reigning paradigm of cosmology may seem ill-conceived at this time. One reads almost daily how astronomers have been able to verify the expansion and cooling predicted by the big bang model with great precision all the way back to the first second after the universe’s creation and have produced detailed portraits of the various stages of its subsequent development. It is important to understand, though, that all these astronomical observations do not prove that the big bang was the beginning. This notion comes from a theoretical extrapolation back to a time beyond what can be observed using the equations of general relativity, Einstein’s theory of gravity that is used to calculate how the expansion of the universe changes with time. The big bang is formally defined as the moment when the equations say that the temperature and density of the universe became infinite, and it is impossible to extrapolate back any further. Concluding that this represents the beginning of all space and time is suspect, however, as Einstein himself once pointed out. Properly construed, finding that the temperature and density become infinite is an indication that the mathematical equations underlying general relativity have become invalid, not that this is when the universe began.

To understand what really happened 14 billion years ago, it is first necessary to have an improved, complete theory of gravity, probably one that incorporates the laws of quantum physics, which Einstein’s theory does not, and a precise understanding of the behavior of matter at high temperatures and pressures. String theory is the leading candidate for such an improved theory of gravity, but it has not developed to the point where it can definitively answer whether the big bang is the beginning or not.

Whether the bang was the beginning of the universe profoundly affects our outlook on its entire history. For example, the conventional assumption—that the big bang is the beginning—immediately forces a series of additional assumptions upon us. To explain why the space-time that emerges from the random, violent quantum creation event becomes remarkably flat and uniform after just one second, as observations show, cosmologists must assume that the bang was immediately followed by a brief period of extraordinarily rapid accelerated expansion, known as inflation. But this early period of accelerated expansion appears to have no connection with a second period of accelerated expansion that began about 9 billion years later, after galaxies and stars had formed. To explain the latter, a further assumption is required: a tiny dollop of dark energy was created at the big bang and only became important after 9 billion years have passed. The result is that today’s big bang model successfully matches all astronomical observations but only by way of an extremely awkward patchwork of assumptions.

Dissatisfaction with this cosmological patchwork has inspired some of us to seek more natural alternatives. To build a new kind of model we had to begin at square one, challenging the key assumption that the big bang is the beginning of space and time. In some models, known as the “pre-big bang” and “ekpyrotic universe,” there is again only a single bang, with a period of contraction preceding it and the current expansion of the universe following it. Another far more elaborate picture is the cyclic model, which proposes that the big bang repeats every trillion years or so leading to the formation of new galaxies, stars, and planets each time. Instead of relying on inflation to smooth out the original random fluctuations, the model has an ultra-slow phase of contraction leading up to each bang that smoothes and flattens the universe naturally. Hence, the cycles are interwoven: The events at the end of one cycle determine the large-scale structure of the universe in the cycle to come.

The ekpyrotic and cyclic models were inspired by the idea, suggested by string theory, that our three-dimensional world is a surface or “brane” embedded in a space (with an extra spatial dimension) separated by a microscopic distance from a second similar brane. A weak, spring-like force holds the two branes together and causes them to smash into one another and bounce apart, perhaps at regular intervals. Each collision is another big bang that produces hot matter and radiation. The branes expand after each collision and the hot matter and radiation spread out. This matter is what ultimately gives rise to galaxies, stars, and planets. The cyclic picture neatly incorporates the mysterious dark matter and dark energy observed in our universe, as well. Dark matter forms at the same time as ordinary matter when the two branes collide. Visible matter is produced on our brane, but invisible or dark matter is produced on the other brane, a leading reason for why we never visibly see it.

Dark energy is the potential energy associated with the spring-like force when the branes move far apart, as they are today. Right after the bang, this potential energy is too small to be significant, but, eventually, billions of years later, it comes to dominate the universe and causes the expansion of our three dimensions to accelerate. As the branes move toward one another, the potential energy decreases, eventually ending the period of accelerated expansion, perhaps after a trillion years. As the branes continue to move toward one another, they remain fully stretched and grow ever smoother and flatter as they head for their next collision. This explains why the universe is so uniform and free of curvature after the bang. When the branes finally collide, they create hot matter and radiation and bounce apart again, starting the next cycle of expansion and cooling.

A key challenge for the new cyclic models is to explain how tiny non-uniformities were generated in the early universe that account for the observed temperature variations in the cosmic background radiation, which are the seeds that formed the galaxies. In the inflationary picture, there is a well-understood explanation for the variations. These non-uniformities are created by quantum fields that permeate all of space and undergo constant random quantum fluctuations. The quantum fluctuations occur spontaneously on subatomic scales and are then rapidly stretched by inflation to enormous distance scales.

In the cyclic picture, the original notion was that the non-uniformities are due to quantum fluctuations that wrinkle the branes and cause different parts of the universe to collide and reheat at slightly different times. Until now, though, many cosmologists have been skeptical about this mechanism, preferring the familiar inflationary model, which works with ordinary space and time rather than a cyclic mechanism that relies on unproven and exotic notions, like extra dimensions and branes.

During just the past few months, though, six different groups of theorists have broken through this conceptual roadblock (cf. references below). They each have introduced versions of the ekpyrotic and cyclic models that can be described in terms of the ordinary fields that physicists are accustomed to, evolving only in the three spatial dimensions we observe. For those who had been skeptical, there is now a convincing calculation that it is possible to produce the observed temperature fluctuations in the cosmic background radiation and the seeds for large-scale structure before the big bang, even if there are not branes and extra dimensions.

Furthermore, three of the groups have constructed versions in which the universe reverses from contraction to expansion phase without encountering a cosmic singularity of any kind—there are no breakdowns in the equations (cf. references 3, 4, and 7). In the higher-dimensional brane picture, this is analogous to avoiding the full collision of the branes by having them repel one another when they get too close and draw apart before they collide. This avoids another common conceptual roadblock, explaining exactly what happens when the branes collide and the extra dimension that separates them disappears.

Suddenly, the possibility that space and time existed before the big bang has become more comprehensible, and perhaps even compelling as a model for our universe. After some initial years of quiet development, there is now a surge of interest in the cyclic possibility, along with new motivations for considering it.

For example, Roger Penrose has argued that a cyclic model may be necessary to explain how the universe is compatible with the second law of thermodynamics, one of the most fundamental dictums of physics. According to the second law, entropy (the amount of disorder) always increases. Since the inflationary model creates an enormous amount of entropy, the universe must have begun with very little before inflation. However, there is no explanation for why this should be so. In fact, cosmologists often describe the universe right after the bang as being chaotic and random, suggesting high entropy. Penrose argues that some event must have preceded the bang to make the entropy low and that this event is likely to repeat in the future. Coming full circle, this seems to result in a cyclic universe.

Turok and I have argued that a cyclic universe also opens a new approach for solving the cosmological constant problem, which many regard as the most challenging in all of physics, if not all of science. The cosmological constant is a form of dark energy that causes the expansion of the universe to accelerate. Observations of supernovae show that the expansion is indeed accelerating today but at an extremely slow pace, doubling in size once every 10 billion years or so. This is possible only if the cosmological constant is 100 orders of magnitude (10100) times smaller than theorists have calculated it should be when the universe was born.

We have proposed that within the model of a cyclic universe the cosmological constant was indeed large in the universe’s distant past, just as theorists estimate, but this was many, many cycles ago. As the cycles of big bangs brought us closer to the present, the cosmological constant gradually relaxed, until finally it reached the small value that astronomers observe today. This idea does not work in the conventional inflationary model of the big bang in which the universe is only 14 billion years old, because the relaxation mechanism that decreases the value of the cosmological constant is too slow. The cyclic model has the advantage over the big bang of being exponentially older, perhaps even eternal. One can further show that, as the cycles proceed, the relaxation slows more and more as the cosmological constant gets smaller, so exponentially more time is spent in cycles with a small cosmological constant. In this picture, it is natural to expect the tiny value for the constant we observe today.

All of these new ideas increase the urgency for the types of measurements that can distinguish between the cyclic and conventional inflationary pictures of our universe. The most promising possibility is the fact that the two models lead to exponentially different predictions for the production of cosmic gravitational waves—ripples that propagate through space and time—in the early universe. These gravitational waves leave a tiny imprint on the pattern of cosmic background radiation received from the early universe that may be detectable through experiments being developed over the next few years. The results of these experiments could finally answer the fundamental questions that we have about our universe, such as where it comes from, and determine once and for all the history and future of the entire cosmos.

[1] A Cyclic Model of the Universe, P. Steinhardt and N. Turok, Science 296: 1436 (2002)
[2] Generating Ekpyrotic Curvature Perturbations Before the Big Bang, J. Lehners, P. McFadden, N. Turok, and P. Steinhardt, arXiv:hep-th/0702153v1
[3] A Smooth Bouncing Cosmology with Scale Invariant Spectrum, P. Creminelli and L. Senatore, arXiv:hep-th/0702165v1
[4] New Ekpyrotic Cosmology, E. Buchbinder, J. Khoury, and B. Ovrut, arXiv:hep-th/0702154v2
[5] Ekpyrotic Collapse with Multiple Fields, K. Koyama and D. Wands, arXiv:hep-th/0703040v2
[6] Scale-invariance in Expanding and Contracting Universes from Two-field Models, A. Tolley and D. Wesley, arXiv:hep-th/0703101v4
[7] On the Transfer of Metric Fluctuations when Extra Dimensions Bounce or Stabilize, T. Battefeld, S. Patil, and R. Brandenberger, Phys. Rev.D 73:086002 (2006)
[8] Before the Big Bang: An Outrageous New Perspective and Its Implications for Particle Physics, R. Penrose, Proceedings of EPAC 2006, Edinburgh Scotland
[9] Turnaround in Cyclic Cosmology, L. Baum and P. Frampton, Phys. Rev. Lett. 98:071301 (2007)
[10] Why the Cosmological Constant is Small and Positive, P. Steinhardt and N. Turok, Science 312: 1180-1182 (2006)

Originally published July 2, 2007

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