sign in sign up
<<
Home , Andrei Linde, Renata Kallosh

The Self-Reproducing Inflationary Recent versions of the inflationary scenario describe the universe as a self-generating fractal that sprouts other inflationary

by

f my colleagues and I are right, we the theory maintains that the ue, which is about 10Ð29 gram per cubic may soon be saying good-bye to the universe was born about 15 billion years centimeter. I idea that our universe was a single ago from a cosmological singularityÑa This and other puzzles forced phys- Þreball created in the big bang. We are state in which the temperature and den- icists to look more attentively at the exploring a new theory based on a 15- sity are inÞnitely high. Of course, one basic assumptions underlying the stan- year-old notion that the universe went cannot really speak in physical terms dard cosmological theory. And we through a stage of inßation. During that about these quantities as being inÞnite. found many to be highly suspicious. I time, the theory holds, the cosmos be- One usually assumes that the current will review six of the most diÛcult. The came exponentially large within an in- laws of physics did not apply then. They Þrst, and main, problem is the very ex- Þnitesimal fraction of a second. At the took hold only after the density of the istence of the big bang. One may won- end of this period, the universe contin- universe dropped below the so-called der, What came before? If space-time ued its evolution according to the big Planck density, which equals about 1094 did not exist then, how could everything bang model. As workers reÞned this grams per cubic centimeter. appear from nothing? What arose Þrst: inßationary scenario, they uncovered As the universe expanded, it gradual- the universe or the laws determining some surprising consequences. One of ly cooled. Remnants of the primordial its evolution? Explaining this initial sin- them constitutes a fundamental change cosmic Þre still surround us in the form gularityÑwhere and when it all beganÑ in how the cosmos is seen. Recent ver- of the microwave background radiation. still remains the most intractable prob- sions of inßationary theory assert that This radiation indicates that the tem- lem of modern . instead of being an expanding ball of perature of the universe has dropped to A second trouble spot is the ßatness Þre the universe is a huge, growing frac- 2.7 kelvins. The 1965 discovery of this of space. suggests that tal. It consists of many inßating balls background radiation by Arno A. Penzi- space may be very curved, with a typical that produce new balls, which in turn as and Robert W. Wilson of Bell Labora- radius on the order of the Planck length, produce more balls, ad inÞnitum. tories proved to be the crucial evidence or 10Ð33 centimeter. We see, however, Cosmologists did not arbitrarily in- in establishing the big bang theory as that our universe is just about ßat on a vent this rather peculiar vision of the the preeminent theory of cosmology. scale of 1028 centimeters, the radius of universe. Several workers, Þrst in Rus- The big bang theory also explained the the observable part of the universe. This sia and later in the U.S., proposed the abundances of hydrogen, helium and result of our observation diÝers from inßationary hypothesis that is the basis other elements in the universe. theoretical expectations by more than of its foundation. We did so to solve 60 orders of magnitude. some of the complications left by the s investigators developed the the- A similar discrepancy between theo- old big bang idea. In its standard form, ory, they uncovered complicat- ry and observations concerns the size A- ed problems. For example, the of the universe. Cosmological examina- standard big bang theory, coupled with tions show that our part of the universe the modern theory of elementary parti- contains at least 1088 elementary parti- ANDREI LINDE is one of the originators cles, predicts the existence of many su- cles. But why is the universe so big? If of inßationary theory. After graduating perheavy particles carrying magnetic one takes a universe of a typical initial from University, he received his chargeÑthat is, objects that have only size given by the Planck length and a Ph.D. at the P. N. Lebedev Physics Insti- tute in Moscow, where he began probing one magnetic pole. These magnetic typical initial density equal to the Planck the connections between particle physics monopoles would have a typical mass density, then, using the standard big and cosmology. He became a professor 1016 times that of the proton, or about bang theory, one can calculate how of physics at in 0.00001 milligram. According to the many elementary particles such a uni- 1990. He lives at Stanford with his wife, standard big bang theory, monopoles verse might encompass. The answer is (also a professor of phys- should have emerged very early in the rather unexpected: the entire universe ics at Stanford), and his sons, Dmitri and evolution of the universe and should should only be large enough to accom- Alex. Besides theorizing about the birth of the cosmos, Linde also dabbles in now be as abundant as protons. In that modate just one elementary particleÑ stage stunts such as sleight-of-hand, ac- case, the mean density of matter in the or at most 10 of them. It would be un- robatics and hypnosis. universe would be about 15 orders of able to house even a single reader of Sci- magnitude greater than its present val- entiÞc American, who consists of about

48 SCIENTIFIC AMERICAN November 1994 Copyright 1994 Scientific American, Inc. SELF-REPRODUCING UNIVERSE in a computer simulation con- sity of the universe there. At the top of the peaks, the colors sists of exponentially large domains, each of which has diÝer- rapidly ßuctuate, indicating that the laws of physics there are ent laws of physics (represented by colors). Sharp peaks are not yet settled. They become Þxed only in the valleys, one of new Òbig bangsÓ; their heights correspond to the energy den- which corresponds to the kind of universe we live in now.

1029 elementary particles. Obviously, universe incorporates important devia- compactiÞcation stopped with four di- something is wrong with this theory. tions from homogeneity, namely, stars, mensions, not two or Þve. The fourth problem deals with the galaxies and other agglomerations of Moreover, the manner in which the timing of the expansion. In its standard matter. Hence, we must explain why the other become rolled up is form, the big bang theory assumes that universe is so uniform on large scales signiÞcant, for it determines the values all parts of the universe began expand- and at the same time suggest some of the constants of nature and the mass- ing simultaneously. But how could all mechanism that produces galaxies. es of particles. In some theories, com- the diÝerent parts of the universe syn- Finally, there is what I call the unique- pactiÞcation can occur in billions of dif- chronize the beginning of their expan- ness problem. captured ferent ways. A few years ago it would sion? Who gave the command? its essence when he said: ÒWhat really have seemed rather meaningless to ask Fifth, there is the question about the interests me is whether God had any why space-time has four dimensions, distribution of matter in the universe. choice in the creation of the world.Ó In- why the gravitational constant is so On the very large scale, matter has deed, slight changes in the physical con- small or why the proton is almost 2,000 spread out with remarkable uniformity. stants of nature could have made the times heavier than the electron. Now Across more than 10 billion light-years, universe unfold in a completely diÝer- developments in its distribution departs from perfect ent manner. For example, many popu- physics make answering these ques- homogeneity by less than one part in lar theories of elementary particles as- tions crucial to understanding the con- 10,000. For a long time, nobody had any sume that space-time originally had struction of our world. idea why the universe was so homoge- considerably more than four dimen- All these problems (and others I have neous. But those who do not have ideas sions (three spatial and one temporal). not mentioned) are extremely perplex- sometimes have principles. One of the In order to square theoretical calcula- ing. That is why it is encouraging that cornerstones of the standard cosmolo- tions with the physical world in which many of these puzzles can be resolved gy was the Òcosmological principle,Ó we live, these models state that the ex- in the context of the theory of the self- which asserts that the universe must be tra dimensions have been Òcompacti- reproducing, inßationary universe. homogeneous. This assumption, how- Þed,Ó or shrunk to a small size and The basic features of the inßationary ever, does not help much, because the tucked away. But one may wonder why scenario are rooted in the physics of el-

Copyright 1994 Scientific American, Inc. SCIENTIFIC AMERICAN November 1994 49 EVOLUTION OF A leads to many inßationary images. In most parts of the universe, the scalar Þeld decreas- domains, as revealed in this sequence of computer-generated es (represented as depressions and valleys). In other places, ementary particles. So I would like to pands and becomes Þlled by various One way to imagine the situation is take you on a brief excursion into this scalar Þelds. The process by which the to picture a ball rolling down the side realmÑin particular, to the uniÞed the- fundamental forces separate is called of a large bowl [see upper illustration on ory of weak and electromagnetic inter- symmetry breaking. The particular val- page 54]. The bottom of the bowl rep- actions. Both these forces exert them- ue of the scalar Þeld that appears in the resents the energy minimum. The posi- selves through particles. Photons medi- universe is determined by the position tion of the ball corresponds to the val- ate the electromagnetic force; the W and of the minimum of its potential energy. ue of the scalar Þeld. Of course, the Z particles are responsible for the weak equations describing the motion of the force. But whereas photons are mass- calar Þelds play a crucial role in scalar Þeld in an expanding universe less, the W and Z particles are extreme- cosmology as well as in particle are somewhat more complicated than ly heavy. To unify the weak and electro- Sphysics. They provide the mecha- the equations for the ball in an empty magnetic interactions despite the obvi- nism that generates the rapid inßation bowl. They contain an extra term corre- ous diÝerences between photons and of the universe. Indeed, according to sponding to friction, or viscosity. This the W and Z particles, intro- general relativity, the universe expands friction is akin to having molasses in duced so-called scalar Þelds. at a rate (approximately) proportional the bowl. The viscosity of this liquid Although scalar Þelds are not the to the square root of its density. If the depends on the energy of the Þeld: the stuÝ of everyday life, a familiar ana- universe were Þlled by ordinary matter, higher the ball in the bowl is, the thick- logue exists. That is the electrostatic then the density would rapidly decrease er the liquid will be. Therefore, if the potentialÑthe voltage in a circuit is an as the universe expanded. Therefore, Þeld initially was very large, the energy example. Electrical Þelds appear only if the expansion of the universe would dropped extremely slowly. this potential is uneven, as it is between rapidly slow down as its density de- The sluggishness of the energy drop the poles of a battery or if the potential creased. But because of the equivalence in the scalar Þeld has a crucial implica- changes in time. If the entire universe of mass and energy established by Ein- tion in the expansion rate. The decline had the same electrostatic potential, stein, the potential energy of the scalar was so gradual that the potential ener- say, 110 volts, then nobody would no- Þeld also contributes to the expansion. gy of the scalar Þeld remained almost tice it; the potential would seem to be In certain cases, this energy decreases constant as the universe expanded. This just another vacuum state. Similarly, a much more slowly than does the densi- behavior contrasts sharply with that of constant scalar Þeld looks like a vacu- ty of ordinary matter. ordinary matter, whose density rapidly um: we do not see it even if we are sur- The persistence of this energy may decreases in an expanding universe. rounded by it. lead to a stage of extremely rapid ex- Thanks to the large energy of the scalar These scalar Þelds Þll the universe pansion, or inßation, of the universe. Þeld, the universe continued to expand and mark their presence by affecting This possibility emerges even if one at a speed much greater than that pre- properties of elementary particles. If a considers the very simplest version of dicted by preinßation cosmological the- scalar Þeld interacts with the W and Z the theory of a scalar Þeld. In this ver- ories. The size of the universe in this particles, they become heavy. Particles sion the potential energy reaches a min- regime grew exponentially. that do not interact with the scalar Þeld, imum at the point where the scalar Þeld This stage of self-sustained, exponen- such as photons, remain light. vanishes. In this case, the larger the sca- tially rapid inßation did not last long. To describe elementary particle phys- lar Þeld, the greater the potential energy. Its duration could have been as short ics, therefore, physicists begin with a According to EinsteinÕs theory of gravi- as 10Ð35 second. Once the energy of the theory in which all particles initially are ty, the energy of the scalar Þeld must Þeld declined, the viscosity nearly dis- light and in which no fundamental dif- have caused the universe to expand very appeared, and inßation ended. Like the ference between weak and electromag- rapidly. The expansion slowed down ball as it reaches the bottom of the netic interactions exists. This diÝerence when the scalar Þeld reached the mini- bowl, the scalar Þeld began to oscillate arises only later, when the universe ex- mum of its potential energy. near the minimum of its potential ener-

50 SCIENTIFIC AMERICAN November 1994 Copyright 1994 Scientific American, Inc. quantum ßuctuations cause the scalar Þeld to grow. In those leading to the creation of inßationary regions. We live in one places, represented as peaks, the universe rapidly expands, of the valleys, where space is no longer inßating. gy. As the scalar Þeld oscillated, it lost more than enough to produce every- common during phase transitions; for energy, giving it up in the form of ele- thing we see now. example, water under the right circum- mentary particles. These particles in- stances remains liquid below zero de- teracted with one another and eventu- nßationary theory did not always grees Celsius. Of course, supercooled ally settled down to some equilibrium look so conceptually simple. At- water eventually freezes. That event temperature. From this time on, the I tempts to obtain the stage of expo- would correspond to the end of the in- standard big bang theory can describe nential expansion of the universe have ßationary period. The idea to use super- the evolution of the universe. a long history. Unfortunately, because cooling for solving many problems of The main diÝerence between inßa- of political barriers, this history is only the big bang theory was exceptionally tionary theory and the old cosmology partially known to American readers. attractive. Unfortunately, as Guth him- becomes clear when one calculates the The first realistic version of the inßa- self pointed out, the postinßation uni- size of the universe at the end of inßa- tionary theory came in 1979 from Alexei verse of his scenario becomes extremely tion. Even if the universe at the begin- A. Starobinsky of the L. D. Landau In- inhomogeneous. After investigating his ning of inßation was as small as 10Ð33 stitute of in Moscow. model for a year, he finally renounced centimeter, after 10Ð35 second of inßa- The Starobinsky model created a sen- it in a paper he co-authored with Erick J. tion this domain acquires an unbeliev- sation among Russian astrophysicists, Weinberg of Columbia University. able size. According to some inßation- and for two years it remained the main In 1982 I introduced the so-called new ary models, this size in centimeters can topic of discussion at all conferences inßationary universe scenario, which equal 10 10 12 Ñthat is, a 1 followed by on cosmology in the . His Andreas Albrecht and Paul J. Steinhardt a trillion zeros. These numbers depend model, however, was rather complicat- of the University of Pennsylvania also on the models used, but in most ver- ed (it was based on the theory of anom- later discovered [see ÒThe Inßationary sions this size is many orders of magni- alies in quantum ) and did not Universe,Ó by Alan H. Guth and Paul J. tude greater than the size of the observ- say much about how inßation could ac- Steinhardt; SCIENTIFIC AMERICAN, May able universe, or 1028 centimeters. tually start. 1984]. This scenario shrugged oÝ the This tremendous spurt immediately In 1981 Alan H. Guth of the Massa- main problems of GuthÕs model. But it solves most of the problems of the old chusetts Institute of Technology sug- was still rather complicated and not cosmological theory. Our universe ap- gested that the hot universe at some very realistic. pears smooth and uniform because all intermediate stage could expand expo- Only a year later did I realize that in- inhomogeneities were stretched 10 10 12 nentially. His model derived from a the- ßation is a naturally emerging feature in times. The density of primordial mono- ory that interpreted the development of many theories of elementary particles, poles and other undesirable ÒdefectsÓ the early universe as a series of phase including the simplest model of the becomes exponentially diluted. (Recent- transitions. This theory was proposed scalar field discussed above. There is no ly we have found that monopoles may in 1972 by David A. Kirzhnits and me need for quantum gravity eÝects, phase inßate themselves and thus eÝectively at the P. N. Lebedev Physics Institute in transitions, supercooling or even the push themselves out of the observable Moscow. According to this idea, as the standard assumption that the universe universe.) The universe has become so universe expanded and cooled, it con- originally was hot. One just considers large that we can now see just a tiny densed into diÝerent forms. Water va- all possible kinds and values of scalar fraction of it. That is why, just like a por undergoes such phase transitions. Þelds in the early universe and then small area on a surface of a huge inßat- As it becomes cooler, the vapor con- checks to see if any of them leads to ed balloon, our part looks ßat. That is denses into water, which, if cooling con- inßation. Those places where inßation why we do not need to demand that all tinues, becomes ice. does not occur remain small. Those do- parts of the universe began expanding GuthÕs idea called for inßation to oc- mains where inßation takes place be- simultaneously. One domain of a small- cur when the universe was in an unsta- come exponentially large and dominate est possible size of 10Ð33 centimeter is ble, supercooled state. Supercooling is the total volume of the universe. Be-

Copyright 1994 Scientific American, Inc. SCIENTIFIC AMERICAN November 1994 51 cause the scalar Þelds can take arbitrary initially it was hot and that the scalar verse can simultaneously resolve many values in the early universe, I called this Þeld from the beginning resided close diÛcult cosmological problems may scenario chaotic inßation. to the minimum of its potential energy. seem too good to be true. Indeed, if all In many ways, chaotic inßation is so Once we began relaxing these assump- inhomogeneities were stretched away, simple that it is hard to understand why tions, we immediately found that inßa- how did galaxies form? The answer is the idea was not discovered sooner. I tion is not an exotic phenomenon in- that while removing previously existing think the reason was purely psycholog- voked by theorists for solving their inhomogeneities, inßation at the same ical. The glorious successes of the big problems. It is a general regime that oc- time made new ones. bang theory hypnotized cosmologists. curs in a wide class of theories of ele- These inhomogeneities arise from We assumed that the entire universe mentary particles. quantum eÝects. According to quantum was created at the same moment, that That a rapid stretching of the uni- mechanics, empty space is not entirely

On the Eighth Day...

he new cosmological theory is highly unusual and, un- the computer shrank down the original image, rather than Tderstandably, may be difficult to picture. One of the expanding the inflating domains.) The images revealed main reasons for the popularity of the old big bang sce- that in the main part of the original domain the scalar field nario is that imagining the universe as a balloon expand- slowly decreases [see illustrations on pages 50 and 51]. ing out in all directions is relatively easy. It is much harder We live in such a part of the universe. Small waves frozen to grasp the structure of an eternally self-replicating frac- on top of an almost homogeneous field eventually give tal universe. Computer simulations can help to some ex- rise to the perturbations in temperature of the background tent. Here I will describe some of these simulations, which radiation the Cosmic Background Explorer satellite discov- I performed with my son Dmitri, now a student at the Cal- ered. Other parts of the picture show growing mountains, ifornia Institute of Technology. which correspond to huge energy densities that lead to ex- We began our simulations with a two-dimensional slice tremely rapid . Hence, one can interpret each peak of the universe filled by an almost homogeneous scalar as a new “big bang” that creates an inflationary “universe.” field. We calculated how the scalar field changed in each The fractal nature of the universe became even more point of our domain after the beginning of inflation. Then apparent after we added in another scalar field. To render we added to this result sinusoidal waves, corresponding things even more interesting, we considered a theory in to the quantum fluctuations that freeze. which the potential energy of this field has three different By continually applying this procedure, we obtained a se- minima, represented as different colors [see illustration on quence of figures that shows the distribution of the scalar page 49]. In a two-dimensional slice of the universe, the field in the inflationary universe. (For viewing purposes, colors near the peaks of the mountains change all the time, indicating that the scalar field is rapid- ly jumping from one energy minimum to another. The laws of physics there are not yet fixed. But in the valleys, where the rate of expansion is slow, the colors no longer fluctuate. We live in one of such domains. Other domains are extremely far away from us. Properties of elementary particles and the laws of their interaction change as one crosses from one domain to another—one should think twice before doing so. In another set of figures, we explored the fractallike nature of the inflationary uni- verse along the lines of a different theory of particle physics. Describing the physical meaning of these images is harder. The strange color pattern (left ) corresponds to the distribution of energy in the theory of axions (a kind of scalar field). We called it a Kandinsky universe, after the famous Rus- sian abstractionist. Seen from a different perspective, the results of our simulations sometimes appear as exploding stars (oppo- site page). We conducted the first series of our simu- lations several years ago after we persuad- ed Silicon Graphics in Los Angeles to loan us one of their most powerful computers for a week. Setting up the simulations was hard work, and only on the seventh day did A ÒKandinskyÓ universe we finish the first series of our calculations

52 SCIENTIFIC AMERICAN November 1994 Copyright 1994 Scientific American, Inc. empty. The vacuum is Þlled with small waves. Once their wavelengths become freeze on top of other frozen waves. At quantum ßuctuations. These ßuctua- suÛciently large, the undulations begin this stage one cannot call these waves tions can be regarded as waves, or un- to ÒfeelÓ the curvature of the universe. quantum ßuctuations anymore. Most of dulations in physical Þelds. The waves At this moment, they stop moving be- them have extremely large wavelengths. have all possible wavelengths and move cause of the viscosity of the scalar Þeld Because these waves do not move and in all directions. We cannot detect these (recall that the equations describing the do not disappear, they enhance the val- waves, because they live only brießy and Þeld contain a friction term). ue of the scalar Þeld in some areas and are microscopic. The Þrst ßuctuations to freeze are depress it in others, thus creating inho- In the inßationary universe the vacu- those that have large wavelengths. As mogeneities. These disturbances in the um structure becomes even more com- the universe continues to expand, new scalar Þeld cause the density perturba- plicated. Inßation rapidly stretches the ßuctuations become stretched and tions in the universe that are crucial for the subsequent formation of galaxies.

n addition to explaining many fea- tures of our world, inßationary the- I ory makes several important and testable predictions. First, inßation pre- dicts that the universe should be ex- tremely ßat. Flatness of the universe can be experimentally veriÞed, because the density of a ßat universe is related in a simple way to the speed of its ex- pansion. So far observational data are consistent with this prediction. Another testable prediction is related to density perturbations produced dur- ing inßation. These density perturba- tions aÝect the distribution of matter in the universe. Furthermore, they may be accompanied by gravitational waves. Both density perturbations and gravita- tional waves make their imprint on the microwave background radiation. They render the temperature of this radia- tion slightly diÝerent in various places in the sky. This nonuniformity is exact- ly what was found two years ago by the Cosmic Background Explorer (COBE ) sat- ellite, a Þnding later conÞrmed by sev- eral other experiments. Although the COBE results agree with the predictions of inßation, it would be premature to claim that COBE has con- An ÒexplosionÓ of the scalar Þeld Þrmed the inßationary theory. But it is certainly true that the results obtained by the satellite at their current level of and saw for the first time all these growing mountains that represent inflation- precision could have deÞnitively dis- ary domains. We were able to fly between them and to enjoy a view of our uni- proved most inßationary models, and verse at the first moments of creation. We looked at the shining screen, and we it did not happen. At present, no other were happy—we saw that the universe is good! But our work did not last long. theory can simultaneously explain why On the eighth day we returned the computer, and the machine’s gigabyte hard the universe is so homogeneous and drive crashed, taking with it the universe that we had created. still predict the Òripples in spaceÓ dis- Now we continue our studies using different methods (and a different Silicon covered by COBE. Graphics computer). But one can play an even more interesting game. Instead Nevertheless, we should keep an open of watching the universe at the screen of a computer, one may try to create the mind. The possibility exists that some universe in a laboratory. Such a notion is highly speculative, to say the least. But new observational data may contradict some people (including Alan H. Guth and me) do not want to discard this possi- inßationary cosmology. For example, if bility completely out of hand. One would have to compress some matter in observations tell us that the density of such a way as to allow quantum fluctuations to trigger inflation. Simple esti- the universe is considerably diÝerent mates in the context of the chaotic inflation scenario suggest that less than one from the critical density, which corre- milligram of matter may initiate an eternal, self-reproducing universe. sponds to a ßat universe, inßationary We still do not know whether this process is possible. The theory of quantum cosmology will face a real challenge. (It fluctuations that could lead to a new universe is extremely complicated. And may be possible to resolve this problem even if it is possible to “bake’’ new universes, what shall we do with them? Can if it appears, but it is fairly complex.) we send any message to their inhabitants, who would perceive their micro- Another complication has a purely scopic universe to be as big as we see ours? Is it conceivable that our own uni- theoretical origin. Inßationary models verse was created by a -hacker? Someday we may find the answers. are based on the theory of elementary particles, and this theory by itself is not

Copyright 1994 Scientific American, Inc. SCIENTIFIC AMERICAN November 1994 53 completely established. Some versions or something very similar to it, is abso- unique features that can be tested (most notably, ) do lutely essential for constructing a con- through observation or experiment. not automatically lead to inßation. Pull- sistent cosmological theory. The inßa- Most, however, are based on the idea of ing inßation out of the superstring mod- tionary theory itself changes as particle chaotic inßation. el may require radically new ideas. We physics theory rapidly evolves. The list should certainly continue the search for of new models includes extended in- ere we come to the most inter- alternative cosmological theories. Many ßation, natural inßation, hybrid inßa- esting part of our story, to the cosmologists, however, believe inßation, tion and many others. Each model has H theory of an eternally existing, self-reproducing inßationary universe. This theory is rather general, but it looks SPACE-TIME FOAM especially promising and leads to the most dramatic consequences in the con- text of the chaotic inßation scenario. PLANCK DENSITY As I already mentioned, one can visu- LARGE alize quantum ßuctuations of the scalar QUANTUM Þeld in an inßationary universe as FLUCTUATIONS waves. They Þrst moved in all possible directions and then froze on top of one another. Each frozen wave slightly in- creased the scalar Þeld in some parts of the universe and decreased it in others. Now consider those places of the uni- INFLATION SMALL QUANTUM verse where these newly frozen waves

POTENTIAL ENERGY FLUCTUATIONS persistently increased the scalar Þeld. Such regions are extremely rare, but still they do exist. And they can be ex- tremely important. Those rare domains HEATING OF UNIVERSE of the universe where the Þeld jumps high enough begin exponentially ex- SCALAR FIELD panding with ever increasing speed. The higher the scalar Þeld jumps, the faster SCALAR FIELD in an inßationary universe can be modeled as a ball rolling down the universe expands. Very soon those the side of a bowl. The rim corresponds to the Planck density of the universe, above rare domains will acquire a much great- which lies a space-time Òfoam,Ó a region of strong quantum ßuctuations. Below the er volume than other domains. rim (green), the ßuctuations are weaker but may still ensure the self-reproduction From this theory it follows that if the of the universe. If the ball stays in the bowl, it moves into a less energetic region universe contains at least one inßation- (orange), where it slides down very slowly. Inßation ends once the ball nears the energy minimum (purple), where it wobbles around and heats the universe. ary domain of a suÛciently large size, it begins unceasingly producing new inßationary domains. Inßation in each particular point may end quickly, but OPEN many other places will continue to ex- INFLATIONARY FLAT UNIVERSE SCENARIO CLOSED pand. The total volume of all these do- mains will grow without end. In essence, one inßationary universe sprouts other inßationary bubbles, which in turn pro- duce other inßationary bubbles [see il- HEATING lustration on opposite page]. UNIVERSE This process, which I have called eter- AT PRESENT TIME nal inßation, keeps going as a chain re- INFLATION action, producing a fractallike pattern of universes. In this scenario the uni- verse as a whole is immortal. Each par- SPACE-TIME FOAM

SIZE OF UNIVERSE STANDARD ticular part of the universe may stem 1012 BIG BANG MODEL 10 from a singularity somewhere in the OPEN past, and it may end up in a singularity FLAT 1030 somewhere in the future. There is, how- PLANCK LENGTH ever, no end for the evolution of the en- tire universe. Ð43 CLOSED Ð35 17 10 10 10 The situation with the very beginning AGE OF UNIVERSE (SECONDS) is less certain. There is a chance that all parts of the universe were created si- EVOLUTION OF THE UNIVERSE diÝers in the chaotic inßation scenario and the multaneously in an initial, big bang sin- standard big bang theory. Inßation increases the size of the universe by 10 10 12, so gularity. The necessity of this assump- that even parts as small as 10Ð33 centimeter (the Planck length) exceed the radius of the observable universe, or 1028 centimeters. Inßation also predicts space to be tion, however, is no longer obvious. mostly ßat, in which parallel lines remain Òparallel.Ó (Parallel lines in a closed uni- Furthermore, the total number of inßa- verse intersect; in an open one, they ultimately diverge.) In contrast, the original tionary bubbles on our Òcosmic treeÓ hot big bang expansion would have increased a Planck-size universe to only 0.001 grows exponentially in time. Therefore, centimeter and would lead to diÝerent predictions about the geometry of space. most bubbles (including our own part

54 SCIENTIFIC AMERICAN November 1994 Copyright 1994 Scientific American, Inc. of the universe) grow indeÞnitely far away from the trunk of this tree. Al- though this scenario makes the exis- tence of the initial big bang almost ir- relevant, for all practical purposes, one can consider the moment of formation of each inßationary bubble as a new Òbig bang.Ó From this perspective, inßa- tion is not a part of the big bang theo- ry, as we thought 15 years ago. On the contrary, the big bang is a part of the inßationary model. In thinking about the process of self- TIME reproduction of the universe, one can- TIME not avoid drawing analogies, however superÞcial they may be. One may won- der, Is not this process similar to what happens with all of us? Some time ago we were born. Eventually we will die, and the entire world of our thoughts, feelings and memories will disappear. But there were those who lived before us, there will be those who will live after, and humanity as a whole, if it is clever enough, may live for a long time. Inßationary theory suggests that a SELF-REPRODUCING COSMOS appears as an extended branching of inßationary similar process may occur with the uni- bubbles. Changes in color represent ÒmutationsÓ in the laws of physics from par- verse. One can draw some optimism ent universes. The properties of space in each bubble do not depend on the time from knowing that even if our civiliza- when the bubble formed. In this sense, the universe as a whole may be stationary, tion dies, there will be other places in the even though the interior of each bubble is described by the big bang theory. universe where life will emerge again and again, in all its possible forms. corresponds to alternative laws of par- geneous, expanding and stationary. Our ould matters become even more ticle interactions. In some inßationary cosmic home grows, ßuctuates and eter- curious? The answer is yes. Until models, quantum ßuctuations are so nally reproduces itself in all possible Cnow, we have considered the strong that even the number of dimen- forms, as if adjusting itself for all pos- simplest inßationary model with only sions of space and time can change. sible types of life that it can support. one scalar Þeld, which has only one If this model is correct, then physics Some parts of the new theory, we minimum of its potential energy. Mean- alone cannot provide a complete expla- hope, will stay with us for years to while realistic models of elementary nation for all properties of our allot- come. Many others will have to be con- particles propound many kinds of sca- ment of the universe. The same physi- siderably modiÞed to Þt with new ob- lar Þelds. For example, in the uniÞed cal theory may yield large parts of the servational data and with the ever theories of weak, strong and electro- universe that have diverse properties. changing theory of elementary parti- magnetic interactions, at least two oth- According to this scenario, we Þnd our- cles. It seems, however, that the past er scalar Þelds exist. The potential ener- selves inside a four-dimensional domain 15 years of development of cosmology gy of these scalar Þelds may have sev- with our kind of physical laws, not be- have irreversibly changed our under- eral diÝerent minima. This condition cause domains with diÝerent dimen- standing of the structure and fate of means that the same theory may have sionality and with alternative proper- our universe and of our own place in it. diÝerent Òvacuum states,Ó correspond- ties are impossible or improbable but ing to diÝerent types of symmetry simply because our kind of life cannot breaking between fundamental interac- exist in other domains. FURTHER READING tions and, as a result, to diÝerent laws Does this mean that understanding PARTICLE PHYSICS AND INFLATIONARY of low-energy physics. (Interactions of all the properties of our region of the COSMOLOGY. Andrei Linde in Physics particles at extremely large energies do universe will require, besides a knowl- Today, Vol. 40, No. 9, pages 61Ð68; Sep- not depend on symmetry breaking.) edge of physics, a deep investigation of tember 1987. Such complexities in the scalar Þeld our own nature, perhaps even includ- THE FRACTAL OF THE INFLA- mean that after inßation the universe ing the nature of our consciousness? TIONARY UNIVERSE. M. Aryal and A. Vil- may become divided into exponentially This conclusion would certainly be one enkin in Physics Letters B, Vol. 199, No. 3, pages 351Ð357; December 24, 1987. large domains that have diÝerent laws of the most unexpected that one could INFLATION AND QUANTUM COSMOLOGY. of low-energy physics. Note that this di- draw from the recent developments in Andrei Linde. Academic Press, 1990. vision occurs even if the entire universe inßationary cosmology. PARTICLE PHYSICS AND INFLATIONARY originally began in the same state, cor- The evolution of inßationary theory COSMOLOGY. Andrei Linde. Harwood responding to one particular minimum has given rise to a completely new cos- Academic Publishers, 1990. of potential energy. Indeed, large quan- mological paradigm, which diÝers con- FROM THE BIG BANG THEORY TO THE tum ßuctuations can cause scalar Þelds siderably from the old big bang theory THEORY OF A STATIONARY UNIVERSE. A. Linde, D. Linde and A. Mezhlumian in to jump out of their minima. That is, and even from the Þrst versions of the Physical Review D, Vol. 49, No. 4, pages they jiggle some of the balls out of their inßationary scenario. In it the universe 1783Ð1826; February 1994. bowls and into other ones. Each bowl appears to be both chaotic and homo-

Copyright 1994 Scientific American, Inc. SCIENTIFIC AMERICAN November 1994 55