The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe - John D. Barrow (2002)

Chapter 8. How Many Vacuums Are There?

“Why is there only one Monopolies Commission?”

Screaming Lord Sutch1

VACUUM LANDSCAPE APPRECIATION

“The Grand Old Duke of York
He had ten thousand men,
He marched them up to the top of the hill,
And he marched them down again.”

Nursery Rhyme

The subtleties and unexpected properties of the quantum vacuum elevated it to play a leading role in fundamental physics in the mid-1970s. Since then its position has become increasingly wide-ranging and pivotal. Every day sees new research papers about some aspect of the vacuum posted on the electronic web sites that physicists use to announce their new work to colleagues all over the world.2 What has given rise to this explosion of interest? The adoption of a definition of the vacuum that requires it to be only a state of minimum energy is the answer. It immediately opens up a number of extraordinary possibilities.

The first question that we might pose about the vacuum as minimum energy state is, ‘Why should there be only one of these minimum energy states?’ The energy ‘landscape’ could contain many undulations, valleys and hills, just like a real terrain. These undulations could be very regular, like a corrugated roof or an egg box, with many different minima, each having the same minimum value for the energy (see Figure 8.1). This scenario suggests two new possibilities: if there can be many vacuums then we have to decide in which one of them our Universe is going to end up; also, we would like to know if it is possible to change vacuums in some way, by jumping from one minimum to the other.

In the example we have drawn in Figure 8.1, the different vacuums correspond to minima of the same depth. We could add a further dimension of possible variation to the situation by marking the position of the vacuum on a two-dimensional surface and its depth by the height above it. This is like a real landscape on the Earth’s surface in which the height above or below sea level defines the altitude at each location. When this extra dimension is added it becomes possible for a continuous line of points to be vacuums at the same height for the system. A simple example is shown in Figure 8.2, where the vacuums form a ring on the floor. In the middle of the ring is a maximum so that the overall shape of the energy landscape is rather like a Mexican hat.

We can imagine still more unusual situations. We have drawn all the minima to lie at the same levels but there is no need for this. The vacuums are just defined by the presence of a local minimum in the landscape. There is no reason why they all need to be at the same level. If there is one which has a lower energy value than the others we will call it the ‘true’ or ‘global’ vacuum. Also, the minima can differ in other, more subtle respects. The curvature of the terrain in their immediate vicinities can be different (see Figure 8.3). So, the terrain can rise steeply or gradually as we move away from the minimum. If you find yourself in a steep-sided vacuum it will be harder to escape compared than from the shallow-sided sort.

Figure 8.1 A vacuum landscape with many local minima of equal depth.

Figure 8.2 A continuous circle of minima of the same depth.

When we looked at some of the effects of vacuum polarisation on the strengths of the measured forces of Nature in the last chapter we saw how the temperature of the environment in which forces act matters. Thus we might well expect that our energy landscapes depend on temperature. As the temperature changes, the shape of the landscape can change very significantly. Both the number of vacuums may change as well as their depths. Some can even cease to be minima if the landscape changes very dramatically.

An interesting example of this process is provided by magnetism. The magnetisation energy of a bar of iron has a pattern of variation that is strongly dependent upon the temperature of the metal. When an iron bar is heated above a particular temperature of 750 degrees Celsius, called the Curie temperature, it displays no magnetic properties. There is no North and South magnetic pole on the bar. The high temperature has randomised the directions of all the atomic configurations in the iron and so there is no overall directionality to the bar’s properties. As the bar is allowed to cool below the Curie temperature a spontaneous magnetisation takes place: the bar ends up with a North magnetic pole at one end and a South magnetic pole at the other. If you repeat this heating and cooling process a number of times you will not necessarily find that the North magnetic pole always lies at the same end of the magnet. We can understand what is happening by looking at the energy landscape above and below the Curie temperature as shown in Figure 8.4.

Figure 8.3 Landscape with different minima and different gradients.

Above the Curie temperature, there is a single minimum vacuum state for the bar. It is symmetrically placed with the minimum at zero so there is no preference for one direction (right) of the bar over another (left). The minimum is a steep-sided valley into which everything will roll no matter where it starts out up the valley and this tells us that it doesn’t matter how our piece of iron started out. Once it is hot enough it will enter this minimum unmagnetised state and lose memory of any previous magnetised state. However, as the bar cools below the Curie temperature something unusual happens. The magnetisation-energy landscape changes from having a single central valley into one with two valleys and a peak in between. The original minimum has turned into a precarious maximum, whilst two new deeper minima have appeared, equidistant on either side of the central maximum. What does this mean for our iron bar? It means that the symmetrical unmagnetised state has become unstable. The system will roll off down into one of the two new minima. There is an equal chance of going either way and this corresponds to the bar being magnetised with the right-hand end or the left-hand end as the magnetic North pole of the resulting bar magnet. This transition from a state where the minimum that the system resides in is symmetric about the zero value to one in which it is asymmetrical is a common phenomenon in Nature and it is called symmetry breaking.

Figure 8.4 The variation of magnetisation of a metal bar with temperature. (a) Above a critical temperature there is a single stable minimum (P) with no preferred directions. (b) Below the critical temperature two minima of equal depth appear and the previous stable minimum turns into an unstable maximum. A point located there will eventually roll into one of the two asymmetrical minima (P and P′) and the bar will have a magnetic North pole at one end and a magnetic South pole at the other.

The phenomenon of symmetry breaking reveals something deeply significant about the workings of the Universe. The laws of Nature are unerringly symmetrical. They do not have preferences for particular times, places and directions. Indeed, we have found that one of the most powerful guides to their forms is precisely such a requirement. Einstein was the first to recognise how this principle had been used only partially by Galileo and Newton. He elevated it to a central requirement for the laws of Nature to satisfy: that they appear the same to all observers in the Universe, no matter how they are moving or where they are located. There cannot be privileged observers for whom everything looks simpler than it does for others. To countenance such observers would be the ultimate anti-Copernican perspective on the Universe.3 This democratic principle is a powerful guide to arriving at the most general expression of Nature’s laws. Yet, despite the symmetry of the laws of Nature, we observe the outcomes of those symmetrical laws to be asymmetrical states and structures. Each of us is a complicated asymmetrical outcome of the laws of electromagnetism and gravity. We occupy particular positions in the Universe at this moment of time even though the laws of gravity and electromagnetism are completely democratic with respect to positions in space. One of Nature’s deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries as the laws themselves. The outcomes are far more complicated, and far less symmetrical, than the laws. Consequently, they are far more difficult to understand. In this way it is possible to have a Universe governed by a very small number of simple symmetrical laws (perhaps just a single law) yet manifesting a stupendous array of complex, asymmetrical states and structures that might even be able to think about themselves. In the last decade, there has been an enormous upsurge of interest in trying to understand the asymmetrical outcomes of symmetrical laws. The availability of inexpensive fast computers has greatly facilitated this activity because the complexities of the asymmetrical outcomes are generally too great for unaided human calculation to reveal what is happening in full detail.

THE UNIFICATION ROAD

“Encyclopaedia Britannica full set, no longer needed due to husband knowing everything.”

Personal ad, Lancashire Post4

The joining together of the forces of Nature is made possible by the variation in their strengths as the temperature rises. This process sees a coming together first of the electromagnetic and weak forces to create a single electroweak force when temperatures reach about 1015 degrees Kelvin. If we carry on charting the strengthening of this force together with the weakening of the strong force, then a second unification is implied when temperatures reach a level of about 1027 degrees Kelvin. Above this so-called ‘grand unification’ temperature there is a single symmetrical force, but below it there is a breaking of this symmetry to create the different strong and electroweak forces.5

This change of symmetry as the temperature falls will be reflected in the behaviour of all the material in the Universe during its very early stages. We can imagine the Universe expanding away from a Big Bang where the initial temperatures and energies are high enough to maintain complete unification of the strengths of the strong and electroweak forces. As the temperature falls below a particular value, these forces separate and go their different ways.

This perspective upon the change of forces during the very early Universe focused the attention of high-energy physicists and cosmologists upon some of the unusual things that might happen if these changes occurred in special ways. In particular, if the elementary particles in the Universe underwent a change of vacuum state, from a high to a low level, then it could make the whole Universe behave in novel and very attractive ways.

In gradually exploring the ramifications of these ideas for the Universe, interest has focused upon the consequences of a hypothetical type of matter existing in the early Universe. In order to avoid being too specific we call this a ‘scalar’ field. This means that at any point of space, and at any time, this field has only one attribute – its magnitude or intensity (a ‘scale’). For example, the density of printer’s ink on this page is a scalar field. The temperature in a room is a scalar field. But wind velocity is not a scalar because it is determined by a magnitude and a direction at every point and moment of time.

In the earliest stages of the Universe’s history the temperature will be very much higher than today and we could expect new forms of matter to be formed which possess a diverse range of vacuum landscapes. Let’s pick on one of these energy fields. This field could have any number of vacuum states of different levels. It need not correspond exactly to any field that we can observe today because it could have decayed away into radiation and other particles during the early stages of the Universe but, ultimately, our unified theory of all the forces of Nature should tell us what it is. Fields like this will possess two types of energy: a kinetic part associated with their motion, and a potential energy associated with their location. A simple analogy is provided by a swinging clock pendulum. When the bob is swinging through its lowest point it is moving at its fastest and its energy is entirely kinetic. As it rises up to its highest point it gradually slows down: its kinetic energy is transformed into potential energy as the bob works to overcome the downward force of gravity. Momentarily, when it stops at its highest point, before beginning its downward motion, its energy is entirely potential.

Energy fields in the early Universe can behave like the pendulum. When the kinetic part of the energy is the largest, the field will change very quickly, but when the potential energy is largest it will change very slowly. Now suppose that the types of changes in the potential shape that we have just been looking at could come into play during the first moments of the Universe’s expansion. The scalar field could begin at high temperatures in a single stable vacuum state like that shown in Figure 8.5, but when the temperature falls below a particular value, Tc, a new vacuum state could appear at much lower energy.

What will happen? If the original vacuum state has a rather shallow gradient around it, then it is possible for the field to respond to all the buffetings and exchanges of energy with other particles and radiation by jumping over the hill and moving off down towards the new minimum. If the transition takes place slowly enough the potential energy of the slowly moving field will hardly be diluted by the expansion of the Universe that is going on all around it. Meanwhile, all the other radiation and energy in the Universe is being rapidly diluted by the expansion and, consequently, the influence of the scalar field can quickly overwhelm everything else and be the dominant form of mass and energy in the Universe. If that happens, there are many dramatic consequences. The expansion of the Universe changes from steady deceleration to acceleration. This new state of affairs arises because the slowly changing scalar field behaves as if it is gravitationally repulsive whereas other forms of matter and radiation are invariably gravitationally attractive. This acceleration will continue for as long as the field rolls very slowly down the potential landscape. Whilst this slow change occurs, the acceleration will produce a very fast fall-off in the radiation temperature of the Universe. Eventually, the acceleration will come to an end. When the scalar field reaches the new vacuum state it will oscillate backwards and forwards many times, gradually losing energy, and decaying into other particles. Huge amounts of energy will be released from these decays and the temperature fall-off of the Universe created by the expansion will be dramatically slowed. The expansion will resume its normal decelerating course (see Figure 8.6).

Figure 8.5 The appearance of a new minimum.

Figure 8.6 The surge in expansion and fall in temperature created by a period of inflation in the early Universe. When inflation ends there is a complicated sequence of events, involving the decay of the scalar field driving the inflation, and the Universe heats up. Subsequently, it cools steadily and continues to expand at a slower rate.

The hypothetical sequence of events we have just traced describes what has become known as cosmological ‘inflation’. Inflation is an interval of cosmic history during which the expansion accelerates. It arises whenever a matter field, like a scalar field, changes very slowly from one vacuum state to another. In fact, it can also occur if there is only one vacuum state, so the potential landscape looks like a very shallow ‘U’ shape. The Russian physicist Andrei Linde,6 now based at Stanford, California, pointed out that as the Universe cools down, a scalar field may just find itself starting to roll down the slope from an energy level high up the hill. If the slope is shallow enough the scalar field will change its energy so slowly that the energy of motion will always be negligible and anti-gravitation and inflation will arise. As physicists started to explore all the different ways in which this phenomenon could occur, it seemed that it was very difficult to avoid it.

The cosmological consequences of changing vacuums are rather extra-ordinary and they have been the focus of cosmologists’ interest since 1981 when the idea was first introduced by the American physicist Alan Guth.7 Our Universe is expanding tantalisingly close to the critical dividing line that separates a future in which the expansion continues for ever from one in which the expansion is eventually reversed into contraction. The ‘critical’, or in-between, universe is very special and it is somewhat mysterious that our Universe is expanding so close to this special trajectory. The universes expanding faster or slower than the critical case tend to diverge further away from the dividing line as time goes on.

In order for our Universe to be still within about twenty per cent of the critical rate after nearly fifteen billion years of expansion it must have begun expanding fantastically close to the critical divide. We know of no reason why it should have begun like that. Inflation offers an appealing explanation. Imagine that the Universe begins expanding in any way we choose, far away from the critical rate. If a scalar matter field exists which ends up rolling towards a lower vacuum state, then the expansion of the Universe will accelerate. For as long as it does, the expansion will be driven very rapidly, closer and closer towards the critical dividing line.

In this way, a very brief interval of inflation is sufficient to drive the expansion so close to the critical divide by the time inflation ends that the subsequent non-inflationary expansion will have a negligible effect on our distance from the critical divide, and we will find ourselves observing a universe that is expanding at a rate within about one part in 100,000 of the critical value.

This is not all. Another mystery of our Universe is the way in which its expansion rate is the same in every direction and from place to place with remarkable precision. If we scan the radiation reaching us from the edge of the visible Universe, we find that its temperature and intensity is the same in every direction to an accuracy of about one part in 100,000. Yet, as we run the history of the Universe backwards, this becomes very hard to understand. Light has not had time to cross from one side of the Universe to the other. There has not been time for differences in the temperature and density of the Universe from one place to another to have been ironed out in the time apparently available. However, if inflation occurred early on, the ensuing surge of accelerated expansion driving the Universe’s infancy allows regions which were large enough to have been spanned by light signals just before inflation commenced, to have grown larger than the entire visible part of the Universe today (Figure 8.7). In the absence of this period of inflationary expansion, those coordinated regions would have grown only to no more than a metre in size today – falling short of an explanation of the extent of the uniformity of the astronomical universe by 1024 metres.

Figure 8.7 Inflation grows a region bigger than the visible part of the Universe today from a region small enough to be coordinated by light signals near the beginning of the expansion. This offers an explanation for the uniformity of the visible Universe today.

Remember that the key idea behind Einstein’s general theory of relativity was that the presence of mass and energy in space will cause it to be curved. This curvature we imagined to be like the undulations caused by heavy objects on a rubber sheet. If the universe is very irregular before inflation begins it is as if the rubber sheet of the universe is very lumpy and bumpy. When inflation begins it creates a stretching effect, driven by the accelerating expansion, which will iron out all the hills and valleys. It will also make the whole sheet look locally rather flat. If you draw a small square on the surface of a balloon as it is inflated then the square will appear to get flatter and flatter as the balloon is inflated. The universe with the critical rate of expansion is one whose space is flat and uncurved at any time. The other universes that expand faster and slower have negatively and positively curved spaces undergoing expansion, respectively. In both cases they will locally look more and more like a flat surface the more inflationary expansion they have experienced. Almost all8 curved surfaces look locally like flat ones when surveyed over small distances.

Inflation kills many birds with one stone. It explains why it is natural for the Universe to be expanding on a trajectory very close to the critical divide today; it explains why the Universe is on average so smooth from place to place and from one direction to another when we survey its density, temperature and expansion rate. Inflation enables the Universe to maintain life-supporting conditions for the billions of years needed for stars to form and biochemical processes to produce replicating molecules and complex organisms. If the expansion had not tracked the critical divide so closely then it would either have peeled off and collapsed back to a big crunch of uninhabitably high density long before stars could form, or it would have expanded so rapidly that neither galaxies nor stars could have condensed out to create the building blocks and stable environments needed for life (Figure 8.8).

Thus, the complexity of the vacuum that makes inflation possible lies at the root of the uniformity of Nature and allows the Universe to persist for billions of years, displaying conditions that are conducive to the formation of stars and biochemical elements.

Figure 8.8 Universes that expand too slowly will collapse back to a big crunch before galaxies can form; universes that expand too quickly do not allow islands of matter to condense out into galaxies and form stars.

VACUUM FLUCTUATIONS MADE ME

“The universe is merely a fleeting idea in God’s mind – a pretty uncomfortable thought, particularly if you’ve just made a down payment on a house.”

Woody Allen9

If the game of musical vacuums that leads to inflation had resulted in a universe that was perfectly smooth and featureless then things would have turned out pretty dull. There would be little to write home about; indeed no one towrite home. Although our Universe is extremely close to uniformity, it is not perfectly so. There are small deviations from uniformity in the density of matter in space in the form of stars and galaxies and great clusters of galaxies – even clusters of clusters.10 In order to explain their presence, we need the expanding Universe to emerge from its early hightemperature history with variations in density that are typically about one part in 100,000 above the average over a wide range of distances. Before the advent of the inflationary theory the source of such irregularities was something of a mystery. Purely random fluctuations were not of the right size, and there were no ideas as to what the origin of the fluctuations might be, let alone their magnitude. Inflation provided a new and compelling possibility that might simultaneously explain the level of the non-uniformities and the way in which they vary with the astronomical scale surveyed.

If we look back at Figure 8.7 we see how inflation may enable us to ‘grow’ the part of the Universe that we can see today from a region small enough for light to travel across it near the beginning of the expansion. The appearance of the fifteen billion light years of space around us today derives from a tiny region. We are its greatly expanded image. If smoothing processes were perfect and that tiny region started off perfectly smooth, then its subsequent inflation would create a large and perfectly smooth region. But, alas, perfectly smooth means no little islands of matter that expand more slowly than the rest, and which break away from the universal expansion to form galaxies and stars which initiate nuclear reactions and the supernovae from which come the biological elements like carbon. All would be cosmic sameness. No structure, no stars, just perfect undisturbed symmetry.

Fortunately for us, this cannot quite be. There must exist fluctuations of quantum uncertainty in the vacuum. The scalar fields whose slow changes can drive the acceleration of the Universe must have zero-point motions. Just as Heisenberg’s Uncertainty Principle forbids us from ever saying that a box is empty, so it forbids us from ever saying that the density or the temperature of the vacuum is perfectly smooth. There must always exist some quantum vacuum fluctuations. So when inflation occurs it will also act upon the very small deviations from perfect uniformity that the zero-point fluctuations create. They will be stretched by the inflationary expansion and left, like scars, on the face of the Universe, tracing small variations in its density and temperature out to the largest astronomical distances. Remarkably, we can predict the form that these fluctuations must take and their fate during the inflation process. These vacuum fluctuations will eventually lead to the aggregation of matter into galaxies and stars, around which planets can form and life can evolve. Without the vacuum the book of life would have only blank pages.

There are two things we need to predict about these stretched vacuum fluctuations: how intense they will be on average and how their undulations should vary with the distance surveyed. Unfortunately, the first of these questions does not yield a clear-cut answer that we can go out and test. Inflation is an appealing idea because the more you look into what will happen to elementary particles during the first moments of the Universe’s expansion the harder it is to avoid inflation. Almost any hypothetical scalar field will do the trick. Inflation is a rather robust consequence that does not depend on very special conditions. However, the intensity of the fluctuations that are dredged up from the vacuum and expanded depends on knowing the mass of the particular scalar matter field that did the inflating. All we can do is reverse-engineer the situation to calculate what intensity level would be needed to grow the galaxies that we see, and determine the mass of scalar field that gets it right. This requires a little work because galaxies do not appear from the fluctuations ready-made. The fluctuations can begin with a very low intensity, but gradually they will become more pronounced. Regions which contain a little more matter than average will attract still more material towards them at the expense of the others – a sort of gravitational Matthew Effect11 that ‘unto he who has shall more be given’, which astronomers call gravitational instability. The process will snowball and eventually produce dense islands of matter in an almost smooth background universe.

Working backwards we can calculate how small the initial non-uniformities need to be if they are to grow into the observed stars and galaxies in the time available since the Universe became cool enough for atoms to form.12 This tells us that the vacuum fluctuations need to be approximately a few parts in 105 in intensity. We have a double check on this from the satellite observations of the microwave background radiation from the Big Bang. The ancient vacuum fluctuations will have left scars in this radiation long before the galaxies ever formed. Astronomers have been searching for these tell-tale imprints from the past ever since the radiation was first discovered in 1965. They have finally been found by NASA’s Cosmic Background Explorer (COBE) satellite orbiting high above the distorting influence of the Earth’s atmosphere. What it sees confirms that fluctuations of the required level were indeed present at the stage when the heat radiation from the Big Bang began its journey towards us. This tiny measured fluctuation level of a few parts in 105, mapped over parts of the sky separated by more than about ten degrees, now acts as a guide to physicists as they try to winnow down the possible scalar matter fields that could have been responsible for inflating the vacuum long ago.

Fortunately, that is not all that can be said. Although we cannot predict the level of the fluctuations expected to emerge from inflation, because it is so sensitive to the identity of the field driving the inflation, we can predict the way in which the pattern of fluctuations should vary with the astronomical scale surveyed. This turns out to be far less sensitive to the identity and properties of the inflating field. There is a simple and most natural case in which the fluctuations have a democratic form, contributing the same curvature of space on every dimension over the very largest astronomical scales. By comparing parts of the sky separated by more than about ten degrees (the face of the full Moon spans about half a degree), the COBE satellite has confirmed these expectations to high accuracy. This is encouraging, but the greatest interest is reserved for much smaller scales which encompass the fluctuations from which the observed clusters and galaxies will have formed. Very recently, these have been extensively mapped for the first time. The results of Boomerang, a balloon experiment launched from the South Pole, show a very close match with the predictions for expanding universes that are very close to the critical divide. In Figure 8.9, the Boomerang results are shown against a continuous curve which is a theoretical prediction of the form expected in a universe that is just slightly denser than the critical value. The key feature that the ob-servers were looking for is the peak in the amplitude of the temperature fluctuation close to separations on the sky of one degree. Its precise location is the most accurate probe of the total density of the Universe. This is the first time that this peak has been unambiguously observed. There is a suggestion that there is a second, lower peak in the data at smaller angles, but more accurate observations will be needed to make a convincing case for its presence.

Figure 8.9 The variation of temperature fluctuations in the microwave background radiation found by the Boomerang project.13 A fit to the data by an almost critical expanding universe’s predictions for these fluctuations is shown. The angular location of the first peak in the fluctuation is our most sensitive probe of the total density of the Universe.

In 2001 a further satellite probe, MAP (the Microwave Background Explorer), will be launched by NASA to pin down the shape of the fluctuation curve with far greater precision over a wider range of sky angles. In 2007, an even more powerful detector, Planck Surveyor, will be launched by the European Space Agency to scrutinise these variations in exquisite detail. The potential pay-off from these two missions is huge. They will enable us to determine whether the distinctive relics of inflation do indeed exist in the Universe and probe directly the vacuum fluctuations emerging from the Big Bang.

These observations become even more powerful cosmological probes when they are combined with the information obtained from the observations of very distant supernovae that we discussed in Chapter 6. In Figure 8.10, the information from both of these observations are shown together. The vertical axis of the graph measures the amount of the energy density in the Universe that can reside in the form of quantum vacuum energy whilst the horizontal axis measures the amount in the form of ordinary matter.

The Boomerang observations are telling us that the Universe lies in the narrow triangular band in the bottom left of the picture, whilst the supernovae observations force it into the oval region lying at right angles to it. The observations pick out areas of the diagram rather than single points or lines because of the measurement uncertainties of the data. Remarkably, the two sets of observations have their largest uncertainties in opposite directions, so in combination they can pin down the Universe by their overlap with far greater uncertainty than when taken singly. We see that the overlap region requires that the vacuum energy contribution to the Universe is very significant. It cannot be anywhere near zero if these observations are both correct.

INFLATION ALL OVER THE PLACE

“I never predict anything and I never will do.”

Paul ‘Gazza’ Gascoigne14

Soon after the benefits of a bout of cosmic inflation were first recognised, it became clear that the consequences were vaster than had been imagined. Suppose that, just before inflation occurred, the Universe was in a pretty chaotic state. It may have contained a huge number of scalar matter fields, all different, some of them possibly affecting one another in complicated ways. Each could have a different potential landscape down which it would fall, starting out at different speeds and slowing at different rates. This anarchic scenario of ‘chaotic’ inflation creates for us a picture of a universe in which every region that is small enough to be smoothed by light signals could have undergone a period of inflation. The amount of inflation that each region will undergo will be random: some regions will experience a lot of inflation and ultimately expand to become very large, whilst others will barely inflate at all and their expansion could be reversed into contraction very soon afterwards. It is like a foam of bubbles being randomly heated so that some of the bubbles expand a lot, others a little. The most short-lived inflationary histories create regions which don’t expand long enough to see stars form and produce the building blocks of life. These still-born ‘bubbles’ will contain no astronomers. Some of the large, long-lived bubbles may expand for billions of years, creating room and time for stars to form the building blocks of biochemical complexity. It is only in one of these big, old bubbles that observers like ourselves can be around to take stock of the cosmic scene.

Figure 8.10 The limits on the relative contributions to the total energy density in the observable Universe contributed by matter (Ωm) and by the vacuum (ΩΛ), the latter in the form of a lambda stress.15 The ‘Supernovae’ region is compatible with observations of the recession of distant supernovae taking part in the expansion of the Universe. The ‘Boomerang’ region is consistent with the Boomerang balloon flight observations of the smallscale fluctuations in the microwave background radiation. The ‘flat’ line separates open universes from closed universes. Also marked is the region which allows the Universe to collapse back to a ‘ big crunch’. This latter region is incompatible with both data sets. The overlap region compatible with Supernovae and Boomerang requires a significant, non-zero contribution by the vacuum energy to the total density of the Universe.

Seen in this light, inflation has an air of inevitability about it. If the Universe is infinite in extent then anything that has any chance of occurring will be occurring somewhere, and so somewhere there will be a region where there is a matter field whose potential-energy landscape is shallow enough for a very slow change to create a lot of accelerated expansion. Even if this is an unlikely situation (although there is no reason to think that it is), it will still happen in some places and we will find ourselves residing in one of them.

This scenario makes our picture of the geography of the Universe vastly more complex. Ever since Copernicus, we have been educated to assume that our location in the Universe is not special. Our observations of the visible Universe show it to be extremely similar from place to place and from one direction to another on average. Copernicus implies that we should see the same level of uniformity on average from any cosmic vantage point. Thus we should expect the Universe to be roughly similar everywhere. There were always sceptics who did not trust this argument and pointed out that we could never be sure that things are not very different in the Universe beyond our visible horizon, fifteen billion light years away. Despite their logical correctness, these commentators had no positive reason for believing that the far-away Universe was different. The chaotic inflationary Universe is revolutionary because for the first time it provides us with a positive reason to expect the Universe to be very different in structure beyond our visible horizon. Even if the Universe did not begin chaotically and there is only one scalar energy field available, the random variations in its behaviour from place to place are enough to create many different inflated regions. At present, we must assume that we can just see the smooth, nearly flat, interior of part of one of them. If we waited long enough, maybe trillions of years in the future, the expansion might reveal the first glimmerings of a region with a quite different structure swimming slowly into view. The little variations in the structure of the vacuum from place to place will have been amplified from microscopic scales to the vastness of extragalactic space. The universality and diversity of the vacuum landscape in the Universe has the scope to expand to become the direct source of the entire cosmic array of light and darkness, space and matter, planets and people. It makes the Universe more complicated than we imagined.

MULTIPLE VACUUMS

“It does not do to leave a dragon out of your calculations, if you live near him.”

J.R.R. Tolkien

We have seen how the valleys of the potential energy landscape can have many different minima. They may all have the same levels or they may be different. The possibility of different vacuum states is far-reaching because if our Universe possesses different possible vacuums it means that the constants of physics, quantities which measure the strengths and properties of the forces of Nature, need not be uniquely determined. They could have fallen out differently, and may even have done so, in some of those distant domains where different amounts of inflation occurred. If the vacuum energy landscape for the Universe has a single minimum then the basic constants of physics and the form of the laws governing the forces of Nature must be the same everywhere.

Let’s look at the situation with many vacuums more closely. Suppose that the early Universe is inhabited by a matter field that moves in a potential energy landscape that is corrugated, with many minima, as in Figure 8.11. Imagine that the cooling down of the Universe, soon after the expansion begins, scatters the field to some random point in this sinuous landscape. It will then start to roll down the slope on which it finds itself towards the local vacuum state. In other parts of the Universe the field will find itself in different valleys and it will end up rolling (perhaps slowly) into a different vacuum state. The consequences of such diversity would be very far-reaching. Each of these vacuums will correspond to a future world with different forces of Nature. One region might inflate into a state in which gravity is the strongest force of Nature that exists. There would be no stars, no nuclear reactions, no chemistry and no life. There is a deep and direct connection between the multiplicity of vacuums and the uniformity in the Universe of those features of its legislation that we have come to call the constants and laws of Nature. This is not the end of it. Even the number of dimensions of space that inflate and become astronomically large can differ from valley to valley along with the constants and forces of Nature. In recent years, physicists have begun to take seriously the possibility that space (and even time) might contain more dimensions than we habitually experience. Somehow physics looks simpler and naturally unified at high temperatures in worlds which possess more than three dimensions. In order to reconcile such a higher dimensional universe with the space that we observe, it is necessary to assume that all but three of the dimensions are imperceptibly small. No one knows how this happens. Perhaps inflation can be selective in some as yet unknown way, allowing only three dimensions of space to inflate and become astronomically large, whilst the others stay imperceptibly small. If a process like this does operate, it might only work when three dimensions become large; or perhaps it is entirely random, so that the number of large dimensions varies all over an infinite universe. Again, we have good reason to believe that living observers will most likely find themselves in a region possessing three large dimensions of space and a single arrow of time. Some of the consequences of different dimensions of space and time are shown in Figure 8.12.

Figure 8.11 A sinuous vacuum landscape with many minima.

Figure 8.12 Universes with different numbers of dimensions of space and time have unusual properties that do not look conducive to complex information-processing and life except when there is one dimension of time and three large dimensions of space.16

Such possibilities change our entire conception of our place in the Universe. We know that our existence is only possible because of a number of fortuitous apparent coincidences between the values of different constants of Nature. If the values of those constants are unchangeably programmed into the formation of the Universe then we might have to conclude that it was rather good luck that they have fallen out to permit life as they have – of course, if they had not done so we would not be here to argue about it.

Alternatively, we might try to argue that life is possible in a multitude of ways other than by means of DNA molecules based upon the properties of elements like carbon, nitrogen and oxygen. Actually, many scientists (including the author) believe that alternative chemical, physical or nanotechnological bases for complexity are very likely, but it is not clear that they can evolve life spontaneously17 on a timescale less than the lifetimes of stars. One day we may develop a form of information processing that is sufficiently complex to merit the name ‘life’ or ‘artificial intelligence’, but it would not have arisen by natural selection alone.

ETERNAL INFLATION

“We know what we are, but know not what we may be.”

William Shakespeare

Soon after it was realised that a ‘chaotic’ vacuum landscape could give rise to different degrees of inflation all over an infinite universe, Andrei Linde and Alex Vilenkin, both Russian physicists now working in America, realised that things could be even more spectacular. These ubiquitous bouts of inflation need not be relegated to some time billions of years in the past. They should be occurring continually throughout the history of the Universe. Even today, most of the Universe beyond our visible horizon is expected to be in a state of accelerating inflation.

Although it appears that our hypothetical scalar field will just roll down the slope of the potential landscape towards the nearest vacuum, the quantum picture of the vacuum introduces tiny fluctuations which make the field zigzag up and down as it moves down the hill. Remarkably, it is very likely that the zigzagging will predominate over the simple downhill rolling and occasionally make the field move up the valley instead of down. It is like a very slowly flowing river moving down a very shallow gradient. In addition to this steady flow there will be a random to-and-fro motion of flotsam on the water surface. If the overall flow is slow enough and the wind strong enough, some of the debris can occasionally move upstream. In the cosmological case this tendency leads to the production of further inflation within sub-domains of the Universe which have already undergone inflation (see Figure 8.13).

Figure 8.13 Eternal inflation.

The spectacular effect of this is to make inflation self-reproducing. Every inflating region gives rise to other sub-regions which inflate and then in turn do the same. The process appears unstoppable – eternal. No reason has been found why it should ever end. Nor is it known if it needs to have a beginning. As with the process of chaotic inflation, every bout of inflation can produce a large region with very different properties. Some regions may inflate a lot, some only a little; some may have many large dimensions of space, some only three; some may contain the four forces of Nature that we see, others may have fewer. The overall effect is to provide a physical mechanism by which to realise all, or at least almost all, possibilities somewhere in a single universe.

This is a striking scenario. It revolutionises our expectations about the complexity of the evolution, past and future, of the Universe in the same way that the possibility of chaotic inflation did for our picture of its geography. There have often been science-fiction stories about all possible worlds displaying all possible permutations of the values of the constants of Nature. But here we have a mechanism that can generate the panoply of choices.

Eternal inflation was not something that cosmologists went out to construct deliberately. It turned up as an inevitable by-product of a theory which offered a straightforward explanation for a number of the observed properties of the Universe. Future astronomical observations will be able to test whether the structure of the radiation fluctuations in the Universe are consistent with inflation having played a decisive role in determining the structure of our visible part of the Universe. So far, unfortunately, the entire grand scheme of eternal inflation does not appear to be open to observational tests. We cannot see further than a distance of about fifteen billion light years. This is the distance that light has had time to travel since the apparent beginning of the expansion that we are now witnessing. The other different domains of inflation will be beyond that horizon. The finiteness of the speed of light insulates us from them. One day, when huge amounts of cosmic time have passed, perhaps the observers of the far future will be privileged to witness the first appearance of one of these strange islands of the Universe, where inflation is still going on or where the laws of physics are very different. Overall, the Universe is likely to be in a steady state, but populated by many little inflating bubbles, each spawning a never-ending sequence of ‘baby universes’. Most of the Universe will be undergoing inflation at the moment. We live in one of the regions where inflation stopped in the past and we could not exist if it were otherwise. An inflating region expands too fast for galaxies and stars to form. Those essential steps in the path towards setting up life-supporting environments must wait until inflation has ended. However, if the Supernova observations are correct we may be witnessing the recent resumption of inflation in our part of the Universe. If so, we don’t know why this is happening.

This revolution in our conception of the Universe sees us as inhabitants of a large domain that has arisen in a cosmic history with neither beginning nor end, where the special requirements for stars and chemistry and life to evolve are met. This local part of the Universe that has inflated to contain our visible portion of the Universe is just part of the story. Else-where, the Universe is predicted to be very different. Globally, our conception of the Universe has been transformed and we must expect that what we can see is not likely to be representative of the whole. All the complexity that we expect to define the totality of the Universe around us is a reflection of the structure of the vacuum. It is a bottomless sea of energy for expanding universes to produce offspring in the form of sub-regions that go their own way, becoming larger and cooler, ultimately creating within themselves the conditions for further baby universes to be born.

At first, these events of inflationary reproduction appear to be spawning something out of nothing. In fact, the situation does nothing of the sort. We might think that if a whole sub-region of universe appears and starts to expand then we must be violating one of the great conservation laws of physics. The most familiar is the conservation of energy. It was discovered in the last century that in all natural processes, the quantity that we call ‘energy’ is conserved. We can change its form, shuffle it around in different ways, use it to turn mass into radiation and vice versa, but when all is said and done, after we do the final accounting we should always find that the total energy comes out the same. So we might think that if we go from ‘no universe’ to ‘universe’ we are getting something – energy – for nothing and our fundamental conservation law is being broken. However, things are not so simple. Energy comes in two forms. Energy of motion is positive but potential forms of energy are negative. The latter is possessed by any body that feels an attractive force, like gravity.

Universes and inflating domains within universes have very surprising properties when we start to inquire about their energies. Einstein’s theory of general relativity ensures that the total of the positive values of the energies of all the masses and motion within them is exactly counterbalanced by the sum of the negative potential energies contributed by the gravitational forces between them. The total energy is zero. An expanding region can appear without any violation of the conservation of energy. This is a rather striking conclusion. It shows how a large amount of inflationary expansion can be underwritten by drawing on a large reservoir of negative potential energy.18

INFLATION AND NEW LAMBDA

“I have yet to see any problem, however complicated, which when you looked at it in the right way, did not become still more complicated.”

Poul Anderson

In Chapter Six we first encountered the deep mystery of the lambda problem. Einstein had found that the force of gravity that Newton uncovered should be partnered by another piece that increases over large distances. Despite later regretting ever letting this genie out of the bag, saying that it was ‘the biggest blunder of my life’, and urging scientists to ignore it, Einstein’s arguments against his creation were never persuasive. In 1947, he wrote despairingly in a letter to his fellow pioneering cosmologist, Georges Lemaître, that

“Since I have introduced this term I have always had a bad conscience. But at that time I could see no other possibility to deal with the fact of the existence of a finite mean density of matter. I found it very ugly indeed that the field force law of gravitation should be composed of two logically independent terms which are connected by addition. About the justification of such feelings concerning logical simplicity it is difficult to argue. I cannot help to feel it strongly that I am unable to believe that such an ugly thing should be realised in Nature.”

You might not like it. You might wish that it would simply go away. But unfortunately, as yet, there seems to be no good reason to exclude it.

Until quite recently, most physicists who worried about this problem were looking for a missing insight to prove that lambda must be zero. They were persuaded of the rightness of this approach by the unnatural situation that is created by the existence of a force like this that ‘just happens’ to become noticeable in the Universe around the epoch when we are living in the Universe, about fourteen billion years after the expansion began. But we have just witnessed a change of attitude. Astronomers have found strong evidence for the existence of a non-zero lambda force. Its size means that it has come to govern the rate at which the Universe is expanding at about the time when galaxies were still forming – what astronomers would call ‘quite recently’. From the theoretician’s point of view this is very odd. Lambda not only exists, but has a special value that makes it come into play near the epoch when life develops in the Universe. The only consolation is that, if these observations are correct, there is now a very special value of lambda to try to explain. The right explanation has a very particular target to shoot at. One can imagine a lot of spurious arguments that manage to ‘explain’ why lambda is zero but not so many that can come up with the unusual observed value.

Inflation has solved a lot of our other puzzles; can it help us with lambda? Unfortunately, it is hard to see how inflation can help. We have already seen how the lambda stress is like a vacuum energy in the Universe. If we look at our potential energy landscape for the scalar field that is driving the inflationary expansion we can relate the presence of lambda to a special property of its topography. In the examples that we have drawn (like Figure 8.5, for example), the level of the minimum that defines the true vacuum state has been placed at a zero value. But there was no reason to do that. It was just artistic licence. The final minimum energy value could have been placed at any level above the zero line. Our knowledge of physics does not tell us where it should be. However, if this level is above the zero line, as in Figure 8.14, then it will leave an energy in the Universe that behaves exactly like the lambda stress. Its height above the zero line will determine the magnitude of the lambda force.

When one looks at the numbers, the situation becomes even more perplexing. The effect of lambda grows steadily with respect to the familiar Newtonian force of gravity as the Universe gets bigger. If it is only recently becoming the dominant force, after billions of years of expansion of the Universe, it must have started out enormously smaller than the Newtonian force. The distance of that final minimum energy level in Figure 8.14 from the zero line in order to explain the value of lambda inferred from the supernova observations is bizarre: roughly 10−120 – that is, 1 divided by 10 followed by 119 zeros! This is the smallest number ever encountered in science.

Figure 8.14 The height of the minimum above the zero line determines the residual value of the lambda stress in the Universe.

Why is it not zero? How can the minimum level be tuned so precisely? If it were 10 followed by just 117 zeros, then the galaxies could not form. Extraordinary fine tuning is needed to explain such extreme numbers. And, if this were not bad enough, the vacuum seems to have its own defence mechanism to prevent us finding easy answers to this problem. Even if inflation does have some magical property which we have so far missed that would set the vacuum energy exactly to zero when inflation ends, it would not stay like that. As the Universe keeps on expanding and cooling it passes through several temperatures at which the breaking of a symmetry occurs in a potential landscape, rather like that which occurs in the example of the magnet that we saw at the beginning of the chapter. Every time this happens, a new contribution to the vacuum energy is liberated and contributes to a new lambda term that is always vastly bigger than our observation allows. And, by ‘vastly bigger’ here, we don’t just mean that it is a few times bigger than the value inferred from observations, so that in the future some small correction to the calculations, or change in the trend of the observations, might make theory and observation fit hand in glove. We are talking about an overestimate by a factor of about 10 followed by 120 zeros! You can’t get much more wrong than that.

All our puzzles about whether or not lambda exists and, if so, what is responsible for giving it such a strange value, are like questions about the inflationary scalar field’s potential landscape. Why is its final vacuum state so fantastically close to the zero line? How does it ‘know’ where to end up when the scalar field starts rolling downhill in its landscape? Nobody knows the answers to these questions. They are the greatest unsolved problems in gravitation physics and astronomy. The nature of their answers could take many forms. There could exist some deep new principle that links together all the different forces of Nature in a way that dictates the vacuum levels of all the fields of energy that feel their effects. This principle would be unlike any that we know because it would need to control all the possible contributions to lambda that arise at symmetry breakings during the expansion of the Universe.19 It would need to control physics over a vast range of energies.

Alternatively, there could be a less principled solution in which the lambda stress is determined completely randomly. Although huge values of lambda are the most probable and persistent, they give rise to a universe that expands too fast too early for stars and galaxies and astronomers ever to appear. If we were casting our eye across all possible universes displaying all possible values of the lambda stress, it could be that those, like our own, with outlandishly small values are self-selected from all the possibilities by the fact that they are the only ones that permit observers to evolve. In fact, if lambda were just one hundred to a thousand times bigger than the observations claim, the sequence of events that led to us might well be prevented. Bigger still and they definitely would be. This type of approach, while it may be true, can never predict or explain the exact value of lambda that we have observed, because life is not so sensitive to the value of lambda that, say, doubling its value would make life impossible.

FALLING DOWNSTAIRS

“… but we shall all be changed, in a moment, in the twinkling of an eye …”

St Paul20

The picture of many vacuums that may characterise the forces and interactions of Nature gives rise to the possibility of inflation. There are many options as to how the change from one ephemerally stable vacuum to another true vacuum might occur and we have no knowledge as yet of the identity of the scalar field which might be the culprit.21 In this way of looking at vacuum, we have so far imagined that the vacuum state in which we now find ourselves is a deep and stable one, a ‘true’ vacuum. The lowest of the low.

What if we are not in such a vacuum basement? It is entirely possible that the state of the Universe in which we find ourselves is that of a temporarily stable, or ‘false’, vacuum. Instead of being on the ground floor of the vacuum landscape, we may be higher up, in a state that is only stable for a period of time. That period is pretty long, because the Universe seems to have possessed the same general laws and properties for about fourteen billion years. But one day things may change very suddenly, without the slightest warning. The situation could be like that pictured in Figure 8.15. If inflation left us lodged in on the shallow ledge in the potential landscape shown in Figure 8.15, then we might suddenly find ourselves nudged over the brink and on the way down to a lower minimum. That nudge might be supplied by very high energy events in the Universe. If collisions between stars or black holes generated cosmic rays of sufficiently high energies, they might be able to initiate the transition to the new vacuum in a region of space.22 The properties of the new vacuum will determine what happens next. We could find ourselves suddenly falling into a vacuum state in which all particles have zero mass and behave like radiation. We would disappear in a flash of light without warning.23 The way in which our form of biochemical life relies on rather particular coincidences between the strengths and properties of the different forces of Nature means that any change of vacuum state would very likely be catastrophic for us. It would leave us in a new world where other forms of life might be possible but there is no reason why they should be a small evolutionary step away from our own biochemical forms.

Figure 8.15 A potential energy landscape with many shallow minima may gradually evolve downstairs from one minimum to another over billions of years. We may not yet have reached the bottom.

This picture of the vacuum landscape is a speculative one. We do not know the overall form of the landscape well enough to be able to tell whether we are already on the ground floor or whether there are other vacuums downstairs into which the states of matter in our locale can fall, either accidentally or deliberately. As one contemplates this radical possibility of an unannounced change in some of the basic properties of the forces of Nature, it is tempting to portray it as the ultimate extension of the idea of punctuated equilibrium that Niles Eldridge and Stephen Jay Gould24 have promoted. They proposed the course of biological evolution by natural selection on Earth proceeds by a succession of slow changes interspersed by sudden jumps rather than as a steady ongoing process. Indeed, we can characterise it as a movement through a landscape with many hills and valleys in which a force is dragging someone along. The pattern of change under these circumstances is for a slow climb up each hill but when the top is reached there will be a sudden jump across to the side of the next hill and another spell of steady hill-climbing (see Figure 8.16). If the Universe follows this lead there may be a shock for our descendants in aeons to come. As with the puzzle of why the lambda force should come into play so close to our time, so we might regard it as unlikely that the epoch at which the fall ‘downstairs’ could occur should be close to the time of human existence in the Universe – unless, of course, there is a link with lambda, or the presence of life can do something inadvertent to precipitate the great fall downstairs. Prophets of doom: do not give up hope.

Figure 8.16 A typical evolution in a landscape with many minima when there is a force acting. The dog climbs the slopes slowly to the top and then suddenly jumps across to a point on the next ascent and begins slowly climbing uphill again.25

BITS OF VACUUM

“Cats, no less liquid than their shadows,
Offer no angles to the wind.
They slip, diminished, neat, through loopholes
Less than themselves.”

A.S.J. Tessimond26

At the start of this chapter, we described a vacuum landscape which was three-dimensional. Imagine a Mexican hat with a shallow valley at the top of the hat and an entire circle of minima all at the same level at the bottom of the hat’s brim, as in Figure 8.2. It is possible to move around the circle of vacuum states in the trough at the bottom of the hat without changing energy. In 1972, the British physicist Tom Kibble27 realised that the possible existence of vacuums with continuous interrelationships of this sort meant that changes in their shape could occur as the Universe cooled, which would create structures in the Universe which retained memory of the energy of the Universe at the time when they formed. They are pieces of vacuum. Depending on the shape and pattern of the possible multiple vacuums they could have three simple forms. There can be lines of vacuum energy, either closed loops or never-ending lines, called ‘cosmic strings’.28 There can be sheets of vacuum energy which extend for ever, called ‘walls’, and there can be finite-sized spherical knots of vacuum energy called monopoles. The strings have a thickness given by the quantum wavelength corresponding to the energy of the Universe when the symmetry breaking that created them took place. Similarly, walls are sheets of vacuum energy with a thickness determined by this quantum wavelength.

These three vacuum structures have proved to be perennially fascinating to astronomers ever since their possible existence was first recognised. It was soon realised that if they could exist then their impacts on the Universe are very different. Walls were only an optional structure in the theories of matter at very high energies that were being explored. This was fortunate because walls are a disaster for the Universe. A single vacuum wall stretched across the visible Universe would exert a devastating gravitational force on the expansion of the Universe and produce huge differences in the intensity of radiation from different directions in the Universe. Evidently, from our observations of the smoothness of the radiation and the expansion, we can conclude that we are not in the presence of cosmic domain walls. This deduction is an example of how an astronomical observation can provide a constraint on the possible properties of the unified theory of the forces of Nature at very high energies which are beyond the reach of the energies attainable by direct experiments.

The next candidate to be considered is the monopole. These are far more problematic. Unlike walls, monopoles appeared to be inevitable in any reasonable theory of how the Universe changed from the hightemperature environment of the Big Bang to the present low-temperature world that we inhabit. If the forces of electricity and magnetism are to exist in our world today then monopoles must be formed in the early Universe. Alas, their presence is another potential disaster. A monopole should form inside every region that light signals have had time to cross from the beginning of the expansion of the universe to the time when the monopoles can appear. Such regions are very small because monopoles are very massive by the standards of elementary particles, and appear in pairs when the universe is very energetic and very young. This means that the region of the universe that eventually expands to become the fifteen-billion light-year expanse that we call the visible Universe today will contain a huge number of these monopoles. When we add up the masses of all the monopoles that we should find, their total mass turns out to be billions of times greater than that of all the stars and galaxies put together. This is not the Universe that we live in. Indeed, it is not a universe that we could live in.

In the mid-1970s, this ‘monopole problem’ was a serious dilemma for physicists trying to develop a unified theory of the different forces of Nature. The candidate theories had many attractive features that offered explanations for particular properties of the Universe, most notably why it displayed such an overwhelming excess of matter over antimatter. But they all predicted a monopole catastrophe. Experimental physicists, on the other hand, didn’t see these monopoles. What happened to them?

It was this problem that first led Alan Guth, then at Stanford University, to the theory of the inflationary Universe. He saw that initiating a period of accelerated expansion would solve the monopole problem in the same way that it solved the problem of the smoothness of the Universe. The inflationary surge of acceleration enabled the whole of our visible Universe to expand from a region that was once small enough for light signals to keep it smooth and coordinated except for the small zero-point fluctuations. A monopole forms every time a mismatch occurs in the direction in which vacuum energy fields are pointing when the universe cools to the energy level of the monopoles. Mismatches produce ‘knots’ in the vacuum energy that manifest themselves as monopoles. These knots can only be ironed out over regions that are small enough for light signals to traverse in the time before the appearance of the monopoles. Guth saw that inflation would enable the whole of our visible Universe today to be encompassed by a region that was once small enough to contain perhaps only one knot of vacuum energy and a single monopole. Their effect on the expansion of our visible Universe would then be utterly negligible and we have a natural explanation for the mysterious cosmic scarcity of monopoles.

What Guth was proposing was that the monopoles are not prevented from forming (as many others were trying to find ways of demonstrating at the time), nor were they annihilated in some way after they formed (as others had also tried to show): they are just moved so far by the expansion that they are beyond the horizon of our visible Universe today. Just as the smoothness of our visible Universe is a reflection of the smoothness of the small domain from which it inflated so its lack of monopoles derives from the smooth, unknotted character of the vacuum fields within the same domain.

Historically, the prime motivation for devising the theory of inflation was the resolution of the monopole problem. An added initial bonus was to provide an explanation for the smoothness and flatness of the visible Universe. However, as time has gone on, the focus of interest has switched to the prediction of inflation that the zero-point fluctuations will be inflated to produce little irregularities from which galaxies can form, for it is here that a critical observational test of the theory will soon be made.

This leaves one more vacuum structure for us to evaluate: the strings. Cosmic strings turn out to be far more interesting than walls or monopoles. Whereas walls and monopoles both threaten to overpopulate the Universe with unwanted mass, and have to be eradicated early on, cosmic strings are more subtle. They will start by threading the Universe with a great network of lines of vacuum energy, like a web of cosmic spaghetti. As the expansion of the Universe proceeds, the network behaves in a complicated fashion. Whenever intersections of string occur, the string reorganises itself by exchanging partners, as shown in Figure 8.17.

The trend is for the network to produce lots of little loops of string at the expense of long lines of string that run across the Universe. Once a small loop is formed it is doomed to dissolve. It will oscillate and wriggle, gradually radiating all its energy away in the form of gravitational waves. If we think of Einstein’s picture of curved space, then the wiggling of the loops of string creates ripples in the geometry, which spread out at the speed of light, taking away the string’s energy like waves on a pond surface. In Figure 8.18 a computer simulation of an expanding box of cosmic strings is shown.

The behaviour of the string network over the history of the Universe is tantalising. It appears that the presence of the loops and lines of string energy can act as seeds around which fluctuations in density can start to develop and from which ultimately galaxies might form. However, it is very difficult to calculate what would happen in detail. A host of complicated processes come into play and the fastest computers in the world are still unable to follow all these processes quickly and accurately enough to determine whether strings can produce real galaxies clustered in the patterns that we see. The acid test of such a theory is again provided by the pattern of fluctuations in the microwave radiation left over from the Big Bang. The gravitational field created by the evolving network of strings will leave its characteristic imprint in this radiation. It appears to have a signature that is quite different from that left by the inflated zero-point fluctuations which provide the rival theory. But not everyone agrees. So far, if the string predictions have been correctly calculated, the evidence of the ground-based detectors is beginning to turn against them, but it is early days. The predictions need to be more fully worked out by bigger computer simulations and elaborated, and only the satellite observations will be fully convincing checks.

Figure 8.17 Cosmic strings exchange loops when they intersect.

Figure 8.18 A computer simulation of a network of cosmic strings in an expanding universe, provided by Paul Shellard.29

The cosmic string scenario for the origin of galaxies is a natural rival to the inflationary theory. In the string theory, the initial non-uniformities in the density of the Universe from place to place are created by the appearance of string loops in different places, from the definite continuous vacuum structure of particular energy fields, whereas in the inflationary theory they arise from the zero-point fluctuations. The two ideas are not natural bed-fellows. Just as inflation sweeps away walls and monopoles that have formed in the Universe so it will sweep away the distribution of cosmic strings if they form before inflation happens. In that case they will play no further role in the formation of galaxies. Thus, if galaxies owe their existence to a population of cosmic strings forming in the very early Universe, either inflation did not happen, and we cannot appeal to any of its other benefits to explain mysterious properties of the Universe, like its proximity to the critical rate of expansion today, or the vacuum structure of the ultimate unified theory has a very peculiar double structure. That structure must undergo a slow change that first enables inflation to occur and then be followed by a further particular type of change which permits cosmic strings to appear without any walls or monopoles appearing along with them. Most cosmologists think that this is a tall order and rather unlikely. However, there is no proof of its impossibility.

Individual cosmic vacuum strings are strange beasts. They could reveal their presence by bending rays of light that move close to them. The defining characteristic of a string is its mass per unit length. The larger this is, the greater will be the mass and gravitational effect of any piece of string on other masses. If a straight line of cosmic string were to pass through this page then its effect on neighbouring masses would be to make them move together. It is as if a wedge is cut out of space around the string and the remaining space pulled together to fill the gap (see Figure 8.19). Strings would be like nothing else we have ever encountered. If a piece of vacuum string extended across a part of space that astronomers were ob-serving then the effect of its gravity would be to behave like a lens. A star lying behind the string would have its image duplicated.30 A curving piece of string would create a tell-tale line of double images. Astronomers have looked for these tell-tale images but have yet to find them. Plenty of multiple images have been seen by the Hubble Space Telescope and they are clearly due to the lensing action of gravity fields. However, they seem to be caused by very large intervening objects like galaxies not cosmic strings.

Figure 8.19 A long cosmic string passing into the page has the same effect as removing a wedge of space around the string. This creates a focusing of light rays as they pass by the string as if they are passing through a lens.

These speculative possibilities show some of the unending richness of the physicists’ conception of the vacuum. It is the basis of our most successful theory of the Universe and why it has the properties that it does. Vacuums can change; vacuums can fluctuate; vacuums can have strange symmetries, strange geographies, strange histories. More and more of the remarkable features of the Universe we observe around us seem to be reflections of these properties of the vacuum. All that remains for us to ask about it is whether it had a beginning and whether it will ever have an end.