The Book of Nothing

by John D. Barrow

  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 c
omplex 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 infl
ationary 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.”