The Endless Universe: A Brief Introduction

Paul J. Steinhardt

Department of Physics, Princeton University, Princeton, NJ 08544,USA

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ABSTRACT.  The cyclic model of the universe" is a radical alternative to standard big bang/inflationary theory in which space and time exist indefinitely, the rapidly accelerating inflationary phase is avoided, and the universe undergoes periodic epochs of expansion and contraction.

Throughout human history, there have been three cosmic paradigms commonly invoked to explain the nature of the universe. Each has been embodied in a modern cosmological model based on Einstein's general theory of relativity.  One is the notion of an Unchanging Universe, which underlies Einstein's static universe model (the first cosmological model proposed after the introduction of General Relativity) and the Steady State Model of Hoyle, Gold and Bondi. This paradigm has been set aside because of Hubble's discovery that the universe is expanding and the discovery by Penzias and Wilson of the cosmic microwave background, direct evidence of an earlier hotter and denser epoch.

The paradigm of a Created Universe, in which space and time spring from nothingness and steadily evolve, underlies today's standard model of cosmology, the big bang/inflationary picture (1-3).  Although the creation process and the first instants are not well understood, the sequence of events following are well-defined and the predictions of the model appear to be in exquisite agreement with current observations.

Finally, we come to the Cyclic Universe, the notion that the universe undergoes periodic epochs of evolution followed by a sequence of events that bring the universe back, phoenix-like, to its initial state. The cyclic concept is at least as old as recorded history. For example, cyclic evolution is an essential part of ancient Hindu cosmology. In the 1920's and 1930's, a version was explored in the context of modern cosmology by Tolman (4) and others.   That version entailed an overdense closed universe in which our three dimensional world expands and contracts at regular intervals.  The idea was set aside because, as Tolman first pointed out, the entropy produced during each cycle would be concentrated during the contracting phase, adding to the entropy produced in earlier phases. The entropy density at the end of each contraction causes the next expansion cycle to be longer than the one before.   The cycles cannot be identical, as originally imagined.  Instead, extrapolating backwards from the present entropy, the universe would have undergone smaller and smaller cycles in the past converging rapidly towards zero duration. The total age of the universe would not be significantly different from a universe with no cycles.  Since the main purpose of considering a cyclic universe is to push back the "beginning" indefinitely, the entropy problem was viewed as a serious impediment and discouraged further work.  Today, we would also discard this idea because it requires an overdense universe, whereas observations inform us that the mass density is only about one-fourth of the critical value required to cycle.

In the last year, however, there has been a return of the Cyclic  Universe in a new 21st century version based on recent ideas developed in fundamental (superstring) physics (5, 6).  The new cyclic universe appears capable of reproducing all of the successful predictions of  the standard big bang/inflationary model with the same exquisite precision even though the key events that shape the large scale structure of the universe occur at different epochs and temperatures and entail different physical processes.

A motivation for considering an alternative is that today's standard model has become more complicated.   The initial big bang model assumed a universe that emerges full of radiation and density and uniformly cools and condenses into structure over time. However, after the big bang, the universe should have been turbulent, chaotic and disordered, whereas  the observed universe seems  remarkably homogeneous and uniform on large scales.  A period of inflationary expansion has been added which stretches the universe at exponentially fast rates, smoothing out the initial inhomogeneities, warps or curvature.  It also leaves behind tiny wrinkles in the distribution of matter and energy that later produce the observed fluctuations in the cosmic microwave background temperature and seed the formation of galaxies. The inflation requires adding a hypothetical field, the inflaton, with special properties that enable it to induce a finite amount of exponential expansion and then decay into particles that form our present universe.  But, adding the inflaton is not enough.  We have recently discovered that we must add yet another component, known as dark energy." Dark energy is different dark matter," which  is  gravitationally self-attractive and joins together with  ordinary matter to form galaxies.  Dark energy is gravitationally self-repulsive and causes the expansion of the universe to accelerate. Recent measurements of the cosmic microwave background  (7) and of  distant supernovae (8, 9, 10) indicate that over 70 percent of the universe consists of dark energy today.  Its existence was not anticipated nor is it explained by the big bang or inflation.  Rather, it is simply an ingredient which must  be added ad hoc in a precise amount to match observations.  We do not know if dark energy is stable or unstable, so we cannot  determine whether the universe will accelerate forever or not.  All told, then, the standard model has required an increasing number of assumptions in the last two decades, not only about there being a beginning of space and time, but also the addition of inflaton fields and dark energy with specially tuned properties.  Seeing these complications inspires the theorist to look for a new approach.

The new cyclic universe model, a model proposed with Neil Turok (Cambridge), turns the conventional picture topsy-turvy (5, 6).  Space and time exist forever. The big bang is not the beginning of time. Rather, it is a bridge to a pre-existing contracting era. The universe undergoes an endless sequence of cycles in which it contracts in a big crunch and re-emerges in an expanding big bang, with trillions of years of evolution in between.  The temperature and density of the universe do not become infinite at any point in the cycle.  Indeed, they never exceed a  finite bound (about a trillion trillion degrees). No high energy inflation has taken place since the big bang. The current homogeneity and  flatness were created by events that occurred before the most  recent big bang. The seeds for galaxy formation were created by  instabilities arising as the universe was collapsing towards a  big crunch, prior to our big bang.

The new cyclic model  is also radically different from the cyclic model discussed by Tolman and others in the 1920's and 1930's or from cyclic models of ages past.  The cycles are not completely independent.  As described above, the key events which set the large scale structure of our present universe occurred a cycle ago, and events that are occurring now are setting the stage for the cycle to come.  The universe is infinite and flat, rather than finite and closed. Because of the flatness, the total energy density in the new cyclic universe  is equal to the critical  value, in accordance with observations. Negative potential energy rather than an overdensity of matter  is what causes the reversal from expansion to contraction.  Right after the bang, the universe undergoes the usual period of radiation and matter domination, followed by a long period of dark energy induced accelerated expansion  (presumably the acceleration that has been recently detected). The accelerated expansion naturally dilutes the density of entropy, black holes and other debris produced in the previous cycle so that the universe  is virtually empty before the next bounce.  During the contraction phase, the matter and radiation density remain infinitesimally small for reasons explained below. So, unlike Tolman's case, the universe is returned to nearly pristine vacuum conditions before the big crunch rather than filled with entropy. During the “bounce” from big crunch to big bang, the density is replenished with new  matter and radiation that serves as the fuel for the subsequent hot big bang phase. New quarks and leptons are created that produce new hydrogen to create new stars. After 15 billion years or so, the dark energy begins to dominate again and cosmic acceleration begins anew until the universe returns to a pristine vacuum once again.

To understand fully how the cyclic model is truly new and different, more details are needed.  Two pedagogical approaches could be considered. One is to adopt ingredients similar to the standard model, such as four dimensions and cosmic fields, to explain the model.  The ingredients are familiar, but the interactions between the fields is very complicated to describe.  Alternatively, we can adopt less familiar ingredients from superstring theory, such as branes, and extra dimensions to describe the model.  These ingredients were not invented for the purpose of this cosmology but were already motivated by fundamental physics.  We choose this approach because, once one gets adjusted to the ingredients, the extra-dimensional description provides a simple and compelling geometrical picture that provides a natural  intuition about how the model works.

In  the superstring picture, our three-dimensional universe is a hypersurface embedded  in a spacetime with an extra spatial dimension of finite extent.  More precisely, our hypersurface is a boundary of the extra dimension separated by a finite  distance from a second hypersurface comprising the other boundary.  The hypersurfaces, known as branes" (short for membranes) have energy and  momentum. They can interact through gravity and exchange virtual membranes.  In the cyclic model, the branes are drawn together by these interactions, and they  collide and bounce at regular  intervals.

The model goes through the following stages.  Each cycle begins with a bang,"   a  collision between branes that creates matter and radiation.  The universe proceeds directly  to the radiation-dominated epoch without encountering any inflation.  The model must introduce a mechanism for making the universe homogeneous, isotropic and flat, and for  creating a nearly scale-invariant spectrum  of density perturbations. However, this will be  accomplished by a sequence of events that occurs at a different point in the cycle.  Hence, the universe proceeds directly after the bang to radiation domination to matter domination  and, finally, to dark energy domination.

In the cyclic model, dark energy moves to center stage as an essential element.  Its source is the potential energy associated with the interaction between branes.   When the branes are far apart, the energy is presumed to be small and positive, acting as a  form of dark energy that causes the branes to stretch at an accelerating rate, expanding by a  factor of two every 14 billion years.  Continued for 100 doublings or about a trillion years, the  dark energy thins out the matter and radiation in the universe to a point where the  spaces approaches a nearly perfect homogeneous vacuum.   Furthermore, any warps or curvature in the branes are stretched out.  Hence,  two of the roles of ultrarapid inflation, making the universe  homogeneous and flat,  are replaced by (ultraslow) dark energy in the cyclic model.  Dark energy also is important in making the cyclic solution a classical attractor.  That is, if the branes are  kicked away from the ideal cyclic orbit,  the period of dark energy domination causes the  evolution to converge after a cycle or two to the ideal evolution (5, 6).

After the matter and radiation have been thinned out, the universe begins a period of contraction."   But, unlike earlier cyclic models discussed in the 1920's and 1930's,  our three dimensions do not contract, so the temperature and density do not diverge. Rather,  the extra dimension between the branes contracts as the two branes approach one  another and head towards collision.  The contraction ends in  a crunch" at which matter  and radiation are created.  The two branes bounce apart, but now filled with the newly created hot matter and radiation whose density dominates the older, thinned out matter-radiation from the  previous cycle.  The new matter and radiation are now the dominant form of energy in the universe, and their gravitation causes the branes to begin to stretch again (and, as a byproduct,  slow down the motion of branes).  The universe has returned to the same state as it was after the last bang and the cycle begins anew.

During the contraction phase, the branes undergo quantum fluctuations that cause them to wrinkle (5, 6, 11).  For simple, exponentially decreasing interbrane potentials, the wrinkles form a  scale-invariant spectrum, remarkably similar to those produced in inflation even those the physical process is completely different.  As a result of the wrinkles, the branes collide, bounce and reheat at different times at different locations.   The collision thereby imprints a scale invariant spectrum  of spatial variations  in the temperature on the branes after the collision. These insure that the cyclic model reproduces the successful inflationary predictions of the temperature variations in the  cosmic microwave background.

There is also an important difference between the predictions of inflation and the cyclic model.  Both models predict a nearly scale-invariant spectrum of temperature fluctuations, but inflation also predicts a nearly scale-invariant spectrum of gravitational waves.  Direct searches for gravitational waves will have to improve several generations before they are sensitive enough to detect these kinds of gravitational waves.  In the short term, the more sensitive test is to search for their imprint on the polarization of the cosmic microwave background.  The background radiation is polarized in part due to the spatial variations in temperature and density. But gravitational waves produce an additional polarization with a distinctive signature.  Polarization experiments are being constructed now that may be sensitive enough to detect the signature. If they are found, then this would support the inflationary picture and definitively rule out the cyclic model.

The new cyclic model has rapidly developed into a promising and provocative alternative to the standard big bang inflationary picture. There remain open issues, most especially a rigorous demonstration that the bounce from contraction to expansion can occur when quantum fluctuations are included. (A related, unproven issue for inflationary cosmology is a rigorous demonstration that the universe emerges from the big bang with the right conditions to have inflation.) The other key aspects of the model are well-developed in technical detail. So, it appears for the next few years, there will be continued development of the models vigorous debates about which  is theoretically preferable. Ultimately, though the  answer must be determined by observation, either the detection  of primordial gravitational waves or of other distinguishing features yet to be determined.   What is at stake is nothing less than our understanding of the past history and future fate of the universe.

Returning to the cosmic paradigms, one observes that the new cyclic model is actually hard to classify.  To a local observer, such as ourselves, each cycle of evolution appears to be identical, and so the “cyclic” appellation seems appropriate.  To a global observer, though, the universe appears to be evolving. More entropy is created each cycle and the net entropy increases from one cycle to the next.  True, the entropy is diluted during the period of dark energy-induced accelerated expansion, so the entropy density returns to (nearly) zero at regular intervals.  However, the total entropy steadily grows, setting a well-defined arrow of time.  Yet  another viewpoint  is obtained by averaging over many cycles.  Then, the cycles appear to be minor modulations on an otherwise steady state.  Hence, the new cyclic model is at once a Cyclic, Evolving and Unchanging Universe, depending on your point of view.  Or, perhaps we should just consider it a new kind of cosmological model for the 21st century.

For more details and updates, see feynman.princeton.edu/~steinh. This work was supported in part by US Department of Energy grant DE-FG02-91ER40671 (PJS).

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