R ESEARCH A RTICLES 8␲G H2 ϭ A Cyclic Model of the Universe 3 1 1 2 ͩ ␾˙ 2 ϩ V ϩ ␤4 ␳ ϩ ␤4 ␳ ͪ (2) Paul J. Steinhardt * and Neil Turok 2 R M a¨ 8␲G We propose a cosmological model in which the universe undergoes an endless ϭϪ a 3 sequence of cosmic epochs that begin with a “bang” and end in a “crunch.” Temperature and density at the transition remain finite. Instead of having an 1 ͩ␾˙ 2 Ϫ V ϩ ␤4 ␳ ϩ ␤4 ␳ ͪ (3) inflationary epoch, each cycle includes a period of slow accelerated expansion R 2 M (as recently observed) followed by contraction that produces the homogeneity, flatness, and energy needed to begin the next cycle. where a dot denotes a derivative with respect to t and H ϵ /a is the Hubble parameter. The The current standard model of cosmology that the universe is flat, rather than closed, equation of motion for ␾ is

(1–4) combines the original big bang mod- based on measurements of the cosmic micro- ˙ 3 ␾¨ ϩ 3H␾ ϭϪV,␾ Ϫ ␤ ␾␤ ␳ el and the inflationary scenario. Inflation, a wave background anisotropy and large-scale , M brief period (10Ϫ30 s) of very rapid cosmic structure. (4) acceleration shortly after the big bang, can In our cyclic model, the universe is infi- and the fluid equation of motion for matter explain the homogeneity and isotropy of nite and flat, rather than finite and closed as (M) or radiation (R) is the universe on large scales (Ͼ100 Mpc), in the oscillatory models. We introduce a ␳ץ ␤ ␳ץ d␳ its spatial flatness, the distribution of gal- negative potential energy rather than spatial i ϭ i ϩ i ϭ ␾ץ ␤ ץ aˆ a axies, and the spatial fluctuations in the curvature to cause the reversal from expan- daˆ a ,␾ i Ϫ ͑␳ ϩ ͒ ϭ cosmic microwave background. However, sion to contraction. Before the reversal, 3 i pi , i M,R (5) the standard model has some cracks. The though, the universe undergoes the usual pe- ϵ ␤ ␾ recent discoveries of cosmic acceleration riod of radiation and matter domination, fol- where aˆ a ( ), pi is the pressure of the ␳ and gravitationally self-repulsive dark en- lowed by a long period of accelerated expan- fluid component with energy density i, and ergy (5–8) were not predicted and have no sion [presumably the acceleration that has “,␾”isd/d␾. The implicit assumption is that 2 particular role in the standard model (1–3). been recently detected (5–8)]. The accelerat- matter and radiation couple to ␤ (␾ )g␮␯ Furthermore, the standard model does not ed expansion, caused by dark energy, is nec- (with scale factor aˆ) rather than the Einstein

explain the “beginning of time,” the initial essary to dilute the entropy, black holes, and metric g␮␯ alone (or the scale factor a). Note conditions of the universe, or what will other debris produced in the previous cycle so that the radiation term in Eq. 1 is actually ␾ ␳ ϰ Ϫ4 happen in the long-term future. that the universe is returned to its original independent of (because R aˆ ) so only ␳ ␾ Here, we present a cosmological model pristine vacuum state before it begins to con- M enters the equation of motion. with an endless sequence of cycles of ex- tract, bounce, and begin a cycle anew. We assume the potential V(␾ ) has the pansion and contraction. By definition, following features, as illustrated in Fig. 1: (i) there is neither a beginning nor end of time, Essential Ingredients V(␾ ) must approach zero rapidly as ␾3 Ϫϱ; nor is there a need to define initial condi- As in inflationary cosmology, the cyclic sce- (ii) the potential must be negative for inter- tions. In addition, we explain the role of nario can be described in terms of the evolu- mediate ␾; and (iii) as ␾ increases, the po- dark matter and generate the homogeneity, tion of a scalar field ␾ along a potential V(␾ ) tential must rise to a shallow plateau with a

flatness, and density fluctuations without in a four-dimensional (4D) quantum field positive value V0. An example of a potential invoking inflation. theory. The essential differences are the form with these properties is The cyclic aspect of the model is reminis- of the potential and the couplings between the Ϫ ␾ V͑␾͒ ϭ V (1Ϫe c ) F(␾) (6) cent of oscillatory models introduced in the scalar field, matter, and radiation. 0 1930s based on a closed universe that under- The analysis of the cyclic model follows where from this point onward we adopt units goes a sequence of expansions, contractions, from the action S that describes gravity, the in which 8␲G ϭ 1. F(␾ ) is a function we and bounces. The oscillatory models were scalar field ␾, and the matter and radiation introduce to ensure that V(␾ )3 0as␾3 constrained by having to pass through a sin- fluids: Ϫϱ. Without loss of generality, we take F(␾ ) gularity in which the energy and temperature to be nearly unity for ␾ to the right of poten- 1 1 ␾͒2 tial minimum. The detailed manner in whichץ͑ diverge. Furthermore, as pointed out by Tol- S ϭ ͵ d4x ͱ Ϫ g ͩ ᏾ Ϫ man (9, 10), entropy produced during one 16␲G 2 it tends to zero at smaller ␾ is not crucial for cycle would add to the entropy produced in the main predictions of the cyclic model. A the next, causing each cycle to be longer than quantitative analysis of this model potential Ϫ V͑␾͒ ϩ ␤4͑␾͒͑␳ ϩ␳͒ͪ (1) the one before it. Extrapolating backward in M R (11) shows that a realistic cosmology can be Ն time, the universe would have to have origi- obtained by choosing c 10 and V0 equal to nated at some finite time in the past so that where g is the determinant of the metric today’s dark-energy density (ϳ6 ϫ 10Ϫ30 3 the problem of explaining the “beginning of g␮␯, G is Newton’s constant, and ᏾ is the g/cm ) in Eq. 6. time” remains. Furthermore, today we know Ricci scalar. The coupling ␤(␾ ) between ␾ We have already mentioned that the cou- ␳ ␳ ␤ ␾ and the matter ( M) and radiation ( R) den- pling ( ) is chosen so that aˆ and, thus, the sities is crucial because it causes the den- matter and radiation density are finite at a ϭ 1Joseph Henry Laboratories, Princeton University, sities to remain finite at the big crunch/big 0. For example, we consider ␤(␾ ) ϳ eϪ␾/͌6 2 Princeton, NJ 08544, USA. Department of Applied bang transition. as ␾3 Ϫϱ. The presence of ␤(␾) and the Mathematics and Theoretical Physics, Center for ␾ Mathematical Sciences, Wilberforce Road, Cambridge The line element for a flat, homogeneous consequent coupling of to nonrelativistic CB3 0WA, UK. universe is Ϫdt2 ϩ a2dx2, where a is the matter represent a modification of Einstein’s *To whom correspondence should be addressed. E- Robertson-Walker scale factor. The equa- theory of general relativity. Because the sca- mail: [email protected] tions of motion following from Eq. 1 are lar field ␾ evolves by an exponentially small

1436 24 MAY 2002 VOL 296 SCIENCE www.sciencemag.org R ESEARCH A RTICLES amount between nucleosynthesis (t ϳ 1s) sometimes called the visible brane. Particles hypothesis (19) that the branes separate after and today (t ϳ 1017 s), the deviations from on the other brane interact only through grav- collision, so the extra dimension immediately standard general relativity are small enough ity with matter on the visible brane and hence reappears. This process cannot be completely to easily satisfy all current cosmological con- behave like dark matter. smooth, because the disappearance of the straints (11). However, the coupling of matter The scalar field ␾ is naturally identified extra dimension is nonadiabatic and leads to to ␾ produces other potentially measurable with the field that determines the distance particle production; that is, the brane colli- effects, including a fifth force that violates between branes. The potential V(␾ )isthe sion is partially inelastic. Preliminary calcu- ␤ the equivalence principle. Provided (ln ),␾ interbrane potential caused by nonperturba- lations of this effect are encouraging, because ϽϽ 10Ϫ3, for today’s value of ␾, these vio- tive virtual exchange of membranes between they indicate that a finite density of particles lations are too small to be detected (11–13). the boundaries. The interbrane force is what is produced (20). The matching condition, We shall assume this to be the case. Hence, causes the branes to repeatedly collide and Eq. 7, parameterizes this effect. Ultimately, a the deviations from general relativity are neg- bounce. At large separation (corresponding to well-controlled string-theoretic calculation ligible today. large ␾ ), the force between the branes should (11, 18, 20) should determine the value of ␹. The final crucial ingredient in the cyclic become small, consistent with the flat plateau model is a matching rule that determines how shown in Fig. 1. Collision corresponds to ␾3 Dark Energy and the Cyclic Model Ϫϱ ϰ ␥␾ to pass from the big crunch to the big bang. . But the string coupling gs e , with The role of dark energy in the cyclic scenario ␾3 Ϫϱ ␥Ͼ The transition occurs as and then 0, so gs approaches zero in this limit is novel. In the standard big bang and infla- rebounds toward positive ␾. Motivated again (18). Nonperturbative effects vanish faster tionary models, the recently discovered dark by string theory (see below), we propose that than any power of gs, for example, as or energy and cosmic acceleration (5–8) are an Ϫ1/g 2 Ϫ1/g some small fraction of the ␾-field kinetic e s,ore s, accounting for the prefactor unexpected surprise with no obvious expla- energy is converted to matter and radiation. F(␾) in Eq. 6. nation. In the cyclic scenario, however, not The matching rule amounts to The coupling ␤(␾ ) also has a natural in- only is the source of dark energy explained, ͱ ␾ ͱ ␾ terpretation in the brane picture. Particles but the dark energy and its associated cosmic ␾˙ e 3/ 2 3 Ϫ ͑1 ϩ ␹͒␾˙ e 3/ 2 (7) reside on the branes, which are embedded in acceleration are actually crucial to the con- where ␹ is a parameter measuring the effi- an extra dimension whose size and warp are sistency of the model; namely, the associated ciency of production of radiation at the determined by ␤. The effective scale factor exponential expansion suppresses density bounce. Both sides of this relation are finite at on the branes is aˆ ϭ a␤(␾ ), not a, and aˆ is perturbations and dilutes entropy, matter, and the bounce. finite at the big crunch or big bang. The black holes to negligible levels. By periodi- function ␤(␾ ) is in general different for the cally restoring the universe to an empty, Stringy Motivation two branes (due to the warp factor) and for smooth state, the acceleration causes the cy- From the perspective of 4D quantum field different reductions of M-theory. However, clic solution to be a stable attractor. theory, the introduction of a scalar field, a the standard Kaluza-Klein behavior ␤(␾ ) ϳ Right after a big bang, the scalar field ␾ is potential, and the couplings to matter in the eϪ␾/͌6 as ␾3 Ϫϱis universal, because the increasing rapidly. However, its motion is cyclic model is no more arbitrary or tuned warp factor becomes irrelevant as the branes damped by the expansion of the universe, and than the requirements for the inflationary approach one another (11, 18). ␾ essentially comes to rest in the radiation- models. However, the ingredients for the cy- Most importantly, the brane-world pro- dominated phase (stage 1 in Fig. 1). There- clic model are also strongly motivated by vides a natural resolution of the cosmic sin- after it remains nearly fixed until the dark string theory and M-theory. This connection gularity (11, 18). One might say that the big energy begins to dominate and cosmic accel- ties our scenario into the leading approach to crunch is an illusion, because the scale factors eration commences. The positive potential fundamental physics and quantum gravity. on the branes (3 aˆ) are perfectly finite there. energy density at the current value of ␾ acts The connection should not be overempha- That is why the matter and radiation densi- as a form of quintessence (21, 22), a time- sized. String theory is not yet proven and ties, and the Riemannian curvature on the varying energy component with negative quantum gravity effects are unimportant for branes, are finite. The only respect in which pressure that causes the present-day acceler- describing cosmology at wavelengths much the big crunch is singular is that the one extra ated expansion. This choice entails tuning V0, longer than a Planck length (10Ϫ33 cm). If the dimension separating the two branes momen- but it is the same degree of tuning required in reader prefers, the connection to string theory tarily disappears. Our scenario is built on the any cosmological model (including inflation) can be ignored. On the other hand, we find the connection useful because it provides a Fig 1. Schematic plot of the po- natural geometric interpretation for the sce- ␾ nario. Hence, we briefly describe the relation. tential V( ) as a function of the field ␾. In M theory, ␾ determines According to M-theory, the universe con- the distance between branes, sists of a 4D “bulk” space bounded by two where ␾3 Ϫϱ as the branes col- 3D domain walls, known as “branes” (short lide. We define ␾ to be zero where for membranes), one with positive and the V(␾ ) crosses zero and, therefore, ␾ other with negative tension (14–17). The is positive when the branes are at branes are free to move along the extra spatial their maximal separation. Far to the right, the potential asymp- dimension, so that they may approach and ␳0 totes to Q, the current value of collide. The fundamental theory is formulat- the quintessence (dark energy) ed in 10 spatial dimensions, but 6 of the density. The solid circles represent dimensions are compactified on a Calabi-Yau the dark energy–dominated stage; manifold, which for our purposes can be the gray circles represent the con- treated as fixed, and therefore ignored. Grav- tracting phase during which densi- ty fluctuations are generated; the ity acts throughout the 5D spacetime, but open circles represent the phase particles of our visible universe are con- when the scalar kinetic energy dominates; and the broken circle represents the stage when the strained to move along one of the branes, universe is radiation dominated. Further details of the sequence of stages are described in the text.

www.sciencemag.org SCIENCE VOL 296 24 MAY 2002 1437 R ESEARCH A RTICLES to explain the recent observations of cosmic tends to zero. After the bounce, radiation is ground (29, 30) is the crucial test for distin- acceleration (5–8). In this case, because the generated and the universe is expanding. At guishing inflation from the cyclic model. dark energy serves several purposes, the sin- first, scalar kinetic energy density (ϰ 1/a6) gle tuning resolves several problems at once. dominates over the radiation (ϰ 1/a4) (stage 6). Cyclic Solution as Cosmic Attractor The cosmic acceleration is nearly 100 or- Soon after, however, the universe becomes ra- Not only do cyclic solutions exist for a range ders of magnitude smaller than considered in diation dominated (stage 7). The motion of ␾ is of potentials and parameters, but they are also inflationary cosmology. Nevertheless, if sus- rapidly damped away, so that it remains close to attractors for a range of initial conditions. The tained for hundreds of e-folds (trillions of its maximal value for the rest of the standard cosmic acceleration caused by the positive- years) or more, the cosmic acceleration can big bang evolution (the next 15 billion years). potential plateau plays the critical role here. flatten the universe and dilute the entropy, Then, the scalar field potential energy begins to For example, suppose the scalar field is jos- black holes, and other debris (neutron stars, dominate, and the field rolls towards Ϫϱ, tled and stops at a slightly different maximal neutrinos, and so forth) created over the pre- where the next big crunch occurs and the cycle value on the plateau compared with the ex- ceding cycle, overcoming the obstacle that begins anew. actly cyclic solution. The same sequence of has blocked previous attempts at a cyclic stages ensues. The scalar field is critically universe. In this picture, we are presently Obtaining Scale-Invariant damped during the exponentially expanding about 14 billion years into the current cycle, Perturbations phase. So by the time the field reaches stage and have just begun the trillions years of One of the most compelling successes of infla- 3, where V ϭ 0, it is rolling almost at the cosmic acceleration. After this amount of tionary theory was to obtain a nearly scale- same rate as if it had started at ␾ϭ0, and accelerated expansion, the number of parti- invariant spectrum of density fluctuations that memory of its initial position has been lost cles in the universe may be suppressed to less can seed large-scale structure (4, 24–26). Here, (11). The argument suggests that it is natural than one per Hubble volume before the cos- the same feat is achieved using different phys- to expect dark energy and cosmic accelera- mic acceleration ends. Ultimately, the scalar ics during an ultraslow contraction phase (stage tion following matter domination in a cyclic field begins to roll back toward Ϫϱ, driving 3 in Fig. 1) (19, 23). In inflation, the density universe, in accordance with what has been the potential to zero. The scalar field ␾ is thus fluctuations are created by very rapid expan- recently observed. the source of the currently observed acceler- sion, causing fluctuations on microscopic scales ation, the reason why the universe is homo- to be stretched to macroscopic scales (4, 24– Comparing Cyclic and Inflationary geneous, isotropic, and flat before the big 26). In the cyclic model, the fluctuations are Models crunch, and the root cause for the universe generated during a quasistatic, contracting uni- The cyclic and inflationary models have nu- reversing from expansion to contraction. verse where gravity plays no significant role merous conceptual differences in addition to (19). Simply because the potential V(␾)isde- those already described. Inflation requires A Brief Tour of the Cyclic Universe creasing more and more rapidly, quantum fluc- two periods of cosmic acceleration: a hypo- Putting together the various concepts that have tuations in ␾ are amplified as the field evolves thetical period of rapid expansion in the early been introduced, we can now present the se- downhill (19, 27, 28). Instabilities in long- universe and the observed current accelera- quence of events in each cycle beginning from wavelength modes occur sooner than those in tion. The cyclic model requires only one pe- the present epoch, stage 1 in Fig. 1. The uni- short-wavelength modes, thereby amplifying riod of acceleration per cycle. verse has completed radiation- and matter-dom- long-wavelength power and, curiously, nearly In the inflationary picture, most of the inated epochs during which ␾ is nearly fixed. exactly mimicking the inflationary effect. The volume of the universe is completely unlike We are presently at the time when its potential nearly scale-invariant spectrum of fluctuations what we see. Even when inflation ends in one energy begins to dominate, ushering in a period in ␾ created during the contracting phase trans- region, such as our own, it continues in oth- of slow cosmic acceleration lasting trillions of form into a nearly scale-invariant spectrum of ers. Because of the superluminal expansion years or more, in which the matter, radiation, density fluctuations in the expanding phase rate of the remaining inflating regions, they and black holes are diluted away and a smooth, (23). Current observations of large-scale struc- occupy most of the physical volume of the empty, flat universe results. Very slowly the ture and fluctuations of the cosmic microwave universe. Regions that have stopped inflating, slope in the potential causes ␾ to roll in the background cannot distinguish between infla- such as our region of the universe, represent negative direction, as indicated in stage 2. Cos- tion and the cyclic model because both predict an infinitesimal fraction. By contrast, the cy- mic acceleration continues until the field nears a nearly scale-invariant spectrum of adiabatic, clic model is one in which the local universe the point of zero potential energy, stage 3. The gaussian density perturbations. is typical of the universe as a whole. All or universe is dominated by the kinetic energy of Future measurements of gravitational waves almost all regions of the universe are under- ␾, but expansion causes this to be damped. may be able to distinguish between the two going the same sequence of cosmic events, Eventually, the total energy (kinetic plus nega- pictures (19). In inflation, where gravity is par- and most of the time is spent in the radiation-, tive potential) reaches zero. From Eq. 2, the amount, quantum fluctuations in all light de- matter-, and dark energy–dominated phases. Hubble parameter is zero and the universe is grees of freedom are subject to the same grav- In the production of perturbations, the momentarily static. From Eq. 3, a¨ Ͻ 0, so that itational effect described above. Hence, not inflationary mechanism relies on stretching a begins to contract. So long as a is nearly only is there a nearly scale-invariant spectrum modes whose wavelength is initially expo- static, the universe satisfies the ekpyrotic con- of energy density perturbations, but there is also nentially sub-Planckian to macroscopic ditions for creating a scale-invariant spectrum a scale-invariant spectrum of gravitational scales. Quantum gravity effects in the initial of density perturbations (19, 23). As the field waves. In the cyclic and ekpyrotic models, state are highly uncertain, and inflationary continues to roll toward Ϫϱ, a contracts and the where the potential, rather than gravity, is the predictions may therefore be highly sensitive kinetic energy of the scalar field grows; that is, cause of the fluctuations, the only field that to sub-Planckian physics. In contrast, pertur- gravitational energy is converted to scalar field obtains a nearly scale-invariant spectrum is the bations in the cyclic model are generated kinetic energy during this part of the cycle. one rolling down the potential, namely ␾, when the modes have wavelengths of thou- Hence, the field races past the minimum of the which only produces energy density fluctua- sands of kilometers, using macroscopic phys- potential and off to Ϫϱ, with kinetic energy tions. The direct search for gravitational waves ics insensitive to quantum gravity effects. becoming increasingly dominant as the bounce or the search for their indirect effect on the The cyclic model deals directly with the nears (stage 5). The scalar field diverges as a polarization of the cosmic microwave back- cosmic singularity, explaining it as a transition

1438 24 MAY 2002 VOL 296 SCIENCE www.sciencemag.org R ESEARCH A RTICLES from a contracting to an expanding phase. Al- 4. J. Bardeen, P. J. Steinhardt, M. S. Turner, Phys. Rev. D Theory, in press (preprint available at http://arXiv.org/ though inflation does not address the cosmic 28, 679 (1983). abs/hep-th/0204091). 5. S. Perlmutter et al., Astrophys. J. 517, 565 (1999). 21. R. R. Caldwell, R. Dave, P. J. Steinhardt, Phys. Rev. Lett. singularity problem directly, it does rely implic- 6. A. G. Riess et al., Astron. J. 116, 1009 (1998). 80, 1582 (1998); see also (21). itly on the opposite assumption: that the big 7. P. M. Garnavich et al., Astrophys. J. 509, 74 (1998). 22. J. Ostriker, P. J. Steinhardt, Sci. Am. 284 (January bang is the beginning of time and that the 8. N. Bahcall, J. P. Ostriker, S. Perlmutter, P. J. Steinhardt, 2001), p. 46. universe emerges in a rapidly expanding state. Science 284, 1481 (1999). 23. J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, Phys. 9. R. C. Tolman, Relativity, Thermodynamics and Cos- Rev. D , in press (preprint available at http:// Inflating regions with high potential energy ex- mology (Oxford Univ. Press, Clarendon Press, Oxford, arXiv.org/abs/hep-th/0109050). pand more rapidly and dominate the universe. If UK, 1934). 24. A. H. Guth, S.-Y. Pi, Phys. Rev. Lett. 49, 1110 (1982). there is a preexisting contracting phase, then the 10. See, for example, R. H. Dicke, J. P. E. Peebles, in 25. A. A. Starobinskii, Phys. Lett. B 117, 175 (1982). General Relativity: An Einstein Centenary Survey,S.H. 26. S. W. Hawking, Phys. Lett. B 115, 295 (1982). high–potential energy regions collapse and dis- Hawking, W. Israel, Eds. (Cambridge Univ. Press, 27. R. Kallosh, L. Kofman, A. Linde, Phys. Rev. D 64, appear before the expansion phase begins. Cambridge, UK, 1979). 123523 (2001). String theory or, more generally, quantum grav- 11. P. J. Steinhardt, N. Turok, Phys. Rev. D, in press 28. J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, High ity can play an important role in settling the (preprint available at http://arXiv.org/abs/ Energy Phys. Theory, in press (preprint available at hep-th/0111098). http://arXiv.org/abs/hep-th/0105212). nature of the singularity and, thereby, distin- 12. T. Damour, A. Polyakov, Nucl. Phys. B 423, 532 29. R. Caldwell, M. Kamionkowski, Sci. Am. (January guishing between the two assumptions. (1994). 2001), p. 46; for a recent discussion see (30). The cyclic model is a complete model of 13. T. Damour, C. R. Acad. Sci., in press (preprint avail- 30. A. Lewis, A. Challinor, N. Turok, Phys. Rev. D 65, able at http://arXiv.org/abs/gr-qc/0109063). 023505 (2002). cosmic history, whereas inflation is only a 14. J. Dai, R. G. Leigh, J. Polchinski, Mod. Phys. Lett. A 4, 31. We thank M. Bucher, S. Gratton, J. Khoury, B. A. theory of cosmic history following an as- 2073 (1989). Ovrut, J. Ostriker, P. J. E. Peebles, A. Polyakov, M. sumed initial creation event. Hence, the cy- 15. P. Horava, E. Witten, Nucl. Phys. B 460, 506 (1996). Rees, N. Seiberg, D. Spergel, A. Tolley, T. Wiseman, 16. ࿜࿜࿜࿜ , Nucl. Phys. B 475, 94 (1996). and E. Witten for useful conversations. We thank L. clic model has more explanatory and predic- 17. J. Polchinski, String Theory (Cambridge Univ. Press, Rocher for pointing out historical references. This tive power. For example, we have already Cambridge, UK, 1998), vols. 1 and 2. work was supported in part by U.S. Department of emphasized how the cyclic model leads nat- 18. J. Khoury, B. A. Ovrut, N. Seiberg, P. J. Steinhardt, N. Energy grant DE-FG02-91ER40671 (P.J.S.) and by urally to the prediction of quintessence and Turok, Phys. Rev. D 65, 086007 (2002). PPARC-UK (N.T.). 19. J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, Phys. cosmic acceleration, explaining them as es- Rev. D 64, 123522 (2001). 1 February 2002; accepted 10 April 2002 sential elements of an eternally repeating uni- 20. H. Liu, G. Moore, N. Seiberg, High Energy Phys. Theory, Published online 2 April 2002; verse. The cyclic model is also inflexible with in press (preprint available at http://arXiv.org/abs/hep- 10.1126/science.1070462 th/0204168); A J. Tolley, N. Turok, High Energy Phys. Include this information when citing this paper. regard to its prediction of no long-wavelength gravitational waves. Inflationary cosmology offers no informa- tion about the cosmological constant prob- Evidence of HIV-1 Adaptation lem. The cyclic model provides a fascinating new twist. Historically, the problem is as- to HLA-Restricted Immune sumed to mean that one must explain why the vacuum energy of the ground state is zero. In the cyclic model, the vacuum energy of the Responses at a Population Level true ground state is not zero. It is negative and Corey B. Moore,1 Mina John,1,2 Ian R. James,1 its magnitude is large, as is apparent from Frank T. Christiansen,2,3 Campbell S. Witt,1,2 Simon A. Mallal1,2* Fig. 1. However, we have shown that the universe does not reach the true ground state. Antigen-specific T cell immunity is HLA-restricted. Human immunodeficiency Instead, it hovers above the ground state from virus–type 1 (HIV-1) mutations that allow escape from host immune responses cycle to cycle, bouncing from one side of the may therefore be HLA allele–specific. We analyzed HIV-1 reverse transcriptase potential well to the other but spending most sequences from a large HLA-diverse population of HIV-1–infected individuals. time on the positive-energy side. Polymorphisms in HIV-1 were most evident at sites of least functional or Reviewing the overall scenario and its im- structural constraint and frequently were associated with particular host plications, what is most remarkable is that the HLA class I alleles. Absence of polymorphism was also HLA allele–specific. cyclic model can differ so much from the stan- At a population level, the degree of HLA-associated selection in viral se- dard picture in terms of the origin of space and quence was predictive of viral load. These results support a fundamental role time and the sequence of cosmic events that for HLA-restricted immune responses in driving and shaping HIV-1 evolution lead to our current universe. Yet, the model in vivo. requires no more assumptions or tunings (and by some measures less) to match the current Selection of viral mutations associated with monkeys challenged with simian-human im- observations. It appears that we now have two loss of antiviral cytotoxic T lymphocyte munodeficiency virus (SHIV) after vaccina- disparate possibilities: a universe with a definite (CTL) responses has been described in hu- tion (4). However, the full extent and im- beginning and a universe that is made and mans with acute and chronic HIV-1 infection portance of CTL escape mutation to HIV-1 remade forever. The ultimate arbiter will be (1), macaques infected with simian immuno- evolution remains to be established. CTL es- nature. Measurements of gravitational waves deficiency virus (SIV) (2, 3), and rhesus cape mutations occur at critical sites within and the properties of dark energy (11) can HLA-restricted CTL epitopes where an provide decisive ways to discriminate between 1Centre for Clinical Immunology and Biomedical Sta- amino acid substitution may abrogate the two pictures observationally. tistics, Royal Perth Hospital and Murdoch University, epitope-HLA binding, reduce T cell receptor Level 2 North Block, Royal Perth Hospital, Wellington recognition, or generate antagonistic CTL re- 2 Street, WA 6000, Australia. Department of Clinical sponses (1). Mutations that affect proteosome Immunology and Biochemical Genetics, Royal Perth References and Notes Hospital. 3Department of Pathology, University of cleavage sites flanking CTL epitopes may 1. A. H. Guth, Phys. Rev. D 23, 347 (1981). Western Australia, WA 6009, Australia. also disrupt cellular processing of the epitope 2. A. D. Linde, Phys. Lett. B 108, 389 (1982). 3. A. Albrecht, P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 *To whom correspondence should be addressed. E- (5). The capacity of the virus to mutate at any (1982). mail: [email protected] amino acid residue is constrained, however,

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