The Book of Nothing

by John D. Barrow

  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 bio
chemical 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 to write 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 fluc
tuation 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.