the right picture, at least back to about onesecond after the big bang. Within only a few hours of the big bang, theproduction of helium and other elements would have stopped. And after that,for the next million years or so, the universe would have just continuedexpanding, without anything much happening. Eventually, once the tempera-ture had dropped to a few thousand degrees, the electrons and nuclei would nolonger have had enough energy to overcome the electromagnetic attractionbetween them. They would then have started combining to form atoms.The universe as a whole would have continued expanding and cooling.However, in regions that were slightly denser than average, the expansionwould have been slowed down by extra gravitational attraction. This wouldeventually stop expansion in some regions and cause them to start to recol-lapse. As they were collapsing, the gravitational pull of matter outside theseregions might start them rotating slightly. As the collapsing region gotsmaller, it would spin faster-just as skaters spinning on ice spin faster as thedraw in their arms. Eventually, when the region got small enough, it would bespinning fast enough to balance the attraction of gravity. In this way, disklikerotating galaxies were born.As time went on, the gas in the galaxies would break up into smaller cloudsthat would collapse under their own gravity. As these contracted, the temper-ature of the gas would increase until it became hot enough to start nuclearreactions. These would convert the hydrogen into more helium, and the heatgiven off would raise the pressure, and so stop the clouds from contracting anyfurther. They would remain in this state for a long time as stars like our sun,burning hydrogen into helium and radiating the energy as heat and light.More massive stars would need to be hotter to balance their stronger gravita-tional attraction. This would make the nuclear fusion reactions proceed somuch more rapidly that they would use up their hydrogen in as little as a hun-dred million years. They would then contract slightly and, as they heated upfurther, would start to convert helium into heavier elements like carbon oroxygen. This, however, would not release much more energy, so a crisis wouldoccur, as I described in my lecture on black holes.What happens next is not completely clear, but it seems likely that the centralregions of the star would collapse to a very dense state, such as a neutron staror black hole. The outer regions of the star may get blown off in a tremendousexplosion called a supernova, which would outshine all the other stars in thegalaxy. Some of the heavier elements produced near the end of the star’s lifewould be flung back into the gas in the galaxy. They would provide some ofthe raw material for the next generation of stars.Our own sun contains about 2 percent of these heavier elements because it isa second- or third-generation star. It was formed some five thousand millionyears ago out of a cloud of rotating gas containing the debris of earlier super-novas. Most of the gas in that cloud went to form the sun or got blown away.However, a small amount of the heavier elements collected together to formthe bodies that now orbit the sun as planets like the Earth.OPEN QUESTIONSThis picture of a universe that started off very hot and cooled as it expanded isin agreement with all the observational evidence that we have today.Nevertheless, it leaves a number of important questions unanswered. First, whywas the early universe so hot? Second, why is the universe so uniform on a largescale-why does it look the same at all points of space and in all directions?Third, why did the universe start out with so nearly the critical rate of expan-sion to just avoid recollapse? If the rate of expansion one second after the bigbang had been smaller by even one part in a hundred thousand millionmillion, the universe would have recollapsed before it ever reached its presentsize. On the other hand, if the expansion rate at one second had been largerby the same amount, the universe would have expanded so much that it wouldbe effectively empty now.Fourth, despite the fact that the universe is so uniform and homogenous on alarge scale, it contains local lumps such as stars and galaxies. These are thoughtto have developed from small differences in the density of the early universefrom one region to another. What was the origin of these density fluctuations?The general theory of relativity, on its own, cannot explain these features oranswer these questions. This is because it predicts that the universe started offwith infinite density at the big bang singularity. At the singularity, general rel-ativity and all other physical laws would break down. One cannot predict whatwould come out of the singularity. As I explained before, this means that onemight as well cut any events before the big bang out of the theory, because theycan have no effect on what we observe. Space-time would have a boundary-a beginning at the big bang. Why should the universe have started off at thebig bang in just such a way as to lead to the state we observe today? Why is theuniverse so uniform, and expanding at just the critical rate to avoid recollapse?One would feel happier about this if one could show that quite a number ofdifferent initial configurations for the universe would have evolved to producea universe like the one we observe.If this is the case, a universe that developed from some sort of random initialconditions should contain a number of regions that are like what we observe.There might also be regions that were very different. However, these regionswould probably not be suitable for the formation of galaxies and stars. Theseare essential prerequisites for the development of intelligent life, at least as weknow it. Thus, these regions would not contain any beings to observe that theywere different.When one considers cosmology, one has to take into account the selectionprinciple that we live in a region of the universe that is suitable for intelligentlife. This fairly obvious and elementary consideration is sometimes called theanthropic principle. Suppose, on the other hand, that the initial state of theuniverse had to be chosen extremely carefully to lead to something like whatwe see around us. Then the universe would be unlikely to contain any regionin which life would appear.In the hot big bang model that I described earlier, there was not enough timein the early universe for heat to have flowed from one region to another. Thismeans that different regions of the universe would have had to have startedout with exactly the same temperature in order to account for the fact that themicrowave background has the same temperature in every direction we look.Also, the initial rate of expansion would have had to be chosen very preciselyfor the universe not to have recollapsed before now. This means that the ini-tial state of the universe must have been very carefully chosen indeed if thehot big bang model was correct right back to the beginning of time. It wouldbe very difficult to explain why the universe should have begun in just thisway, except as the act of a God who intended to create beings like us.THE INFLATIONARY MODELIn order to avoid this difficulty with the very early stages of the hot big bangmodel, Alan Guth at the Massachusetts Institute of Technology put forward anew model. In this, many different initial configurations could have evolved tosomething like the present universe. He suggested that the early universe mighthave had a period of very rapid, or exponential, expansion. This expansion issaid to be inflationary-an analogy with the inflation in prices that occurs to agreater or lesser degree in every country. The world record for price inflationwas probably in Germany after the first war, when the price of a loaf of breadwent from under a mark to millions of marks in a few months. But the inflationwe think may have occurred in the size of the universe was much greater eventhan that-a million million million million million times in only a tiny frac-tion of a second. Of course, that was before the present government.Guth suggested that the universe started out from the big bang very hot. Onewould expect that at such high temperatures, the strong and weak nuclearforces and the electromagnetic force would all be unified into a single force.As the universe expanded, it would cool, and particle energies would go down.Eventually there would be what is called a phase transition, and the symmetrybetween the forces would be broken. The strong force would become differentfrom the weak and electromagnetic forces. One common example of a phasetransition is the freezing of water when you cool it down. Liquid water is sym-metrical, the same at every point and in every direction. However, when icecrystals form, they will have definite positions and will be lined up in somedirection. This breaks the symmetry of the water.In the case of water, if one is careful, one can “supercool” it. That is, one canreduce the temperature below the freezing point-0 degrees centigrade-with-out ice forming. Guth suggested that the universe might behave in a similarway: The temperature might drop below the critical value without the symme-try between the forces being broken. If this happened, the universe would bein an unstable state, with more energy than if the symmetry had been broken.This special extra energy can be shown to have an antigravitational effect. Itwould act just like a cosmological constant.Einstein introduced the cosmological constant into general relativity when hewas trying to construct a static model of the universe. However,in this case,the universe would already be expanding. The repulsive effect of this cosmo-logical constant would therefore have made the universe expand at an ever-increasing rate. Even in regions where there were more matter particles thanaverage, the gravitational attraction of the matter would have been out-weighed by the repulsion of the effective cosmological constant. Thus, theseregions would also expand in an accelerating inflationary manner.As the universe expanded, the matter particles got farther apart. One would beleft with an expanding universe that contained hardly any particles. It wouldstill be in the supercooled state, in which the symmetry between the forces isnot broken. Any irregularities in the universe would simply have beensmoothed out by the expansion, as the wrinkles in a balloon are smoothedaway when you blow it up. Thus, the present smooth and uniform state of theuniverse could have evolved from many different nonuniform initial states.The rate of expansion would also tend toward just the critical rate needed toavoid recollapse.Moreover, the idea of inflation could also explain why there is so much matterin the universe. There are something like 1,080 particles in the region of theuniverse that we can observe. Where did they all come from? The answer isthat, in quantum theory, particles can be created out of energy in the form ofparticle/antiparticle pairs. But that just raises the question of where the energycame from. The answer is that the total energy of the universe is exactly zero.The matter in the universe is made out of positive energy. However, the mat-ter is all attracting itself by gravity. Two pieces of matter that are close to eachother have less energy than the same two pieces a long way apart. This isbecause you have to expend energy to separate them. You have to pull againstthe gravitational force attracting them together. Thus, in a sense, the gravita-tional field has negative energy. In the case of the whole universe, one canshow that this negative gravitational energy exactly cancels the positive ener-gy of the matter. So the total energy of the universe is zero.Now, twice zero is also zero. Thus, the universe can double the amount of pos-itive matter energy and also double the negative gravitational energy withoutviolation of the conservation of energy. This does not happen in the normalexpansion of the universe in which the matter energy density goes down as theuniverse gets bigger. It does happen, however, in the inflationary expansion,because the energy density of the supercooled state remains constant while theuniverse expands. When the universe doubles in size, the positive matter ener-gy and the negative gravitational energy both double, so the total energyvery large amount. Thus, the total amount of energy available to make parti-cles becomes very large. As Guth has remarked, “It is said that there is no suchthing as a free lunch. But the universe is the ultimate free lunch.”THE END OF INFLATIONThe universe is not expanding in an inflationary way today. Thus, there hadto be some mechanism that would eliminate the very large effective cosmolog-ical constant. This would change the rate of expansion from an acceleratedone to one that is slowed down by gravity, as we have today. As the universeexpanded and cooled, one might expect that eventually the symmetry betweenthe forces would be broken, just as supercooled water always freezes in the end.The extra energy of the unbroken symmetry state would then be released andwould reheat the universe. The universe would then go on to expand and cool,just like the hot big bang model. However, there would now be an explanationof why the universe was expanding at exactly the critical rate and why differ-ent regions had the same temperature.In Guth’s original proposal, the transition to broken symmetry was supposed tooccur suddenly, rather like the appearance of ice crystals in very cold water.The idea was that “bubbles” of the new phase of broken symmetry would haveformed in the old phase, like bubbles of steam surrounded by boiling water.The bubbles were supposed to expand and meet up with each other until thewhole universe was in the new phase. The trouble was, as I and several otherpeople pointed out, the universe was expanding so fast that the bubbles wouldbe moving away from each other too rapidly to join up. The universe would beleft in a very nonuniform state, with some regions having symmetry betweenthe different forces. Such a model of the universe would not correspond towhat we see.In October 1981 I went to Moscow for a conference on quantum gravity. Afterthe conference, I gave a seminar on the inflationary model and its problems atthe Sternberg Astronomical Institute. In the audience was a young Russian,Andrei Linde. He said that the difficulty with the bubbles not joining up couldbe avoided if the bubbles were very big. In this case, our region of the universecould be contained inside a single bubble. In order for this to work, the changefrom symmetry to broken symmetry must have taken place very slowly insidethe bubble, but this is quite possible according to grand unified theories.Linde’s idea of a slow breaking of symmetry was very good, but I pointed outthat his bubbles would have been bigger than the size of the universe at thetime. I showed that instead the symmetry would have broken everywhere atthe same time, rather than just inside bubbles. This would lead to a uniformuniverse, like we observe. The slow symmetry breaking model was a goodattempt to explain why the universe is the way it is. However, I and severalother people showed that it predicted much greater variations in themicrowave background radiation than are observed. Also, later work castdoubt on whether there would have been the right kind of phase transition inthe early universe. A better model, called the chaotic inflationary model, wasintroduced by Linde in 1983. This doesn’t depend on phase transitions, and itcan give us the right size of variations of the microwave background. The infla-tionary model showed that the present state of the universe could have arisenfrom quite a large number of different initial configurations. It cannot be thecase, however, that every initial configuration would have led to a universelike the one we observe. So even the inflationary model does not tell us whythe initial configuration was such as to produce what we observe. Must we turnto the anthropic principle for an explanation? Was it all just a lucky chance?That would seem a counsel of despair, a negation of all our hopes of under-standing the underlying order of the universe.QUANTUM GRAVITYIn order to predict how the universe should have started off, one needs laws thathold at the beginning of time. If the classical theory of general relativity wascorrect, the singularity theorem showed that the beginning of time would havebeen a point of infinite density and curvature. All the known laws of sciencewould break down at such a point. One might suppose that there were new lawsthat held at s