The most dramatic consequence of Einstein’s general theory of relativity was its prediction that the entire universe should be expanding. By this, we mean that if we could measure the separation of distant clusters of galaxies we would find their separation tomorrow to be greater than it is today. Nevertheless, I am not expanding, the Earth is not expanding, nor is our galaxy. These structures do not expand because they are bound together by stronger local forces of chemical or gravitational origin. Only when we reach the scale of great clusters of galaxies do we find the markers that participate in the expansion of the universe. The first solutions of Einstein’s equations which displayed this expansion were found in the early 1920s by the young St Petersburg mathematician and pioneer meteorologist, Alexander Friedmann. These “Friedmann universes” still provide us with the best description of the overall structure of the universe and its expansion in time.

Seven years after Friedmann’s theoretical deductions, Edwin Hubble found convincing observational evidence that the universe was indeed expanding. The spectra of light from stars in distant galaxies were shifted systematically in the direction of the red end of the optical spectrum when compared with the same spectral lines measured on Earth. There was a simple interpretation for the systematic shift of lines of all wavelengths towards lower energies. It was analogous to the well-known Doppler shift whereby waves emitted by a receding source are received less frequently than waves emitted by a stationary or approaching source. By measuring the frequency shift it was possible to deduce the recession speed of the light source. By comparing objects of the same intrinsic brightness it was possible to infer their relative distances from us by measuring their apparent brightness. The result was Hubble’s famous expansion “law”, showing the speed of expansion of the universe increasing with distance.

The expansion means that the average conditions in the universe change continuously. The temperature and density of matter were greater in the past than today. Astronomers have gradually pieced together a pleasingly consistent picture for the universal history that unfolds as the universe expands (figure 1).

 

We live about 14 billion years after the expansion of the universe appears to have begun, unless some unknown physics intervenes in the split second close to the beginning to make things different. However, we are able to produce a well-tested model of the early universe back to a time that lies just one second after the apparent beginning. The density of matter is still little more than that of water at that time. Remarkably, when the universe is between one second and three minutes old it behaves like a vast nuclear reactor, producing the light isotopes of deuterium, helium-3, helium-4, and lithium-7 in abundances that correspond closely to those observed around the universe today. These detailed astronomical observations allow us to confirm the consistency of our model of the universe right back to these very early times. Likewise, the existence of the microwave background radiation – its thermal spectrum, dipole temperature variation, and flat spectrum of large-scale temperature fluctuations (all observed with great precision by the COBE satellite and by ground-based and air-borne observations) – confirm the general picture of the hot early universe. Before one second we need a fuller description of the behavior and identity of elementary particles of matter than we possess at present. When the universe is younger than about 10–10 seconds, it experiences extremes of temperature and energy that exceed any we can produce on Earth in particle colliders at CERN.

This overall scenario of expansion from a hot early state to a cooler present state is usually referred to as the Big Bang model and is accepted as the working picture for the evolution of the universe by almost all cosmologists. Many aspects of its evolution (even at very late stages) are still uncertain and detailed variants of the Big Bang model are actively explored to discover which can provide the best explanation for the origin of galaxies. 

Big and old, dark and cold

One of the curious features of the universe is the way in which it presents us with an environment that is superficially so hostile to life. But again, appearances can be deceptive. We know that the universe is expanding and therefore its huge size is a consequence of its great age. And any universe that contains the building blocks of complexity must be old enough for stars to form and generate the elements on which such complexity is based. This requires elements heavier than hydrogen and helium, which are formed in the first three minutes of the Big Bang. The heavier biochemical elements, such as carbon, are made from them by nuclear reactions in the stars. When stars die these biochemical elements are dispersed into space and find their way into planets and ultimately into people.

This process of nuclear alchemy is long and slow. It takes billions of years to run its course. Thus a universe that contains “observers” must be billions of years old and hence billions of light years in size. These are necessary conditions for life to be possible. Further consequences then follow. The large size of a habitable universe ensures that it has a very low average density and so galaxies and stars are widely separated. Outposts of life are likely to be separated by vast astronomical distances, ensuring that development occurs in isolation from other outposts of life, at least until technical knowledge is sophisticated. The large amount of expansion also ensures that the universe is very cold. This, in turn, means that the night sky appears dark. There is too little energy density in the universe to make it bright. Thus universes that meet the necessary conditions for life are big and old, dark and cold.

One might speculate that these aspects of the universes (which should be universal features for observers everywhere) play a significant role in shaping our religious and philosophical impressions of the universe and our place within it. Again, we stress how deceptive appearances can be. Many philosophers have appealed to the vastness and sparseness of the universe as evidence for its basic dysteleological character. Yet the discovery of the expansion of the universe shows how subtle this matter is. Those aspects of the universe, which, to some commentators, appear so obviously in conflict with any interpretation of the universe as hospitable for life, turn out to be crucial features that are necessary for a universe to support complexity of any known sort.  

It is worth looking a little more closely at the emptiness of space. If we were to smooth out all the matter in the universe into a smooth sea of evenly spaced particles, there would be only about one atom in every cubic meter of space – a far better vacuum than could ever be created in a laboratory on Earth. If we gather the matter into clumps then this density corresponds to about one Earth-sized planet in every cube of side 10 light years, one star in every cube of side 1000 light years, one galaxy of 100 billion stars in every cube of side 10 million light years. Faced with these numbers we begin to see why there seem to be so few extraterrestrials about: in a universe that is big enough and old enough to give rise to life, the average distances between planets and stars are necessarily huge. In any expanding universe there is a simple approximate relationship G_ρt² ≈ 1 between the age of the universe, t, and the density of matter, ρ, mediated only by Newton’s constant of gravitation, G. This relation, as Gerald Whitrow (in Mascall 1956) was the first to stress, ensures that there is an unbreakable link between local environmental conditions in the universe and its global structure.

Simple inflation

The expansion of the universe is delicately poised, very close to the critical dividing line that separates universes that are expanding fast enough to keep going forever from those that will ultimately contract back towards a cataclysmic Big Crunch in the future. Indeed, so close are we to this critical divide that our observations cannot tell us for sure what the long-range forecast holds. However, it is the very proximity of the expansion to the watershed that is the big mystery: a priori it seems highly unlikely to arise by chance. Again, this is not totally unexpected: universes that expand too fast are unable to aggregate material into galaxies and stars, so the building blocks of complex life cannot be made. By contrast, universes that expand too slowly end up collapsing into contraction before the billions of years needed for stars to form have passed. Only universes close to the critical divide can live long enough and expand gently enough for the stars and planets to form (figure 2).
        

                       

Since 1980, there has been an explanation for the universe’s proximity to the critical divide and its very large size (Guth 1981). These are features that can be explained by a sequence of events that may be very probable in any type of universe, no matter how it starts out expanding. This so called “inflationary” theory of the very early universe introduces a slight gloss on the simple picture of an expanding universe. The standard Big Bang picture of the expanding universe that has been with us since the 1920s has a particular property: the expansion is decelerating. No matter whether the universe is destined to expand forever, or to collapse back to a Big Crunch, the expansion is always decelerated by the gravitational attraction of its material contents.

It had generally been assumed that gravity is always attractive. But in the 1970s, particle physicists began to find that their theories predicted the existence at high energies of many new forms of matter, called “scalar fields”, whose gravitational effect upon each other was repulsive (Barrow 1994). If those fields were to become the largest contributors to the density of the universe at some stage in its very early history, then the deceleration of the universe would be replaced by a surge of acceleration. Remarkably, it seems that if particular scalar fields do exist, then they invariably come to be the most influential constituent of the universe, and their influence only ceases when they decay away into ordinary matter and radiation.

The inflationary universe hypothesis is simply that such a brief period of accelerated expansion occurred early in the history of the universe (see figure 3).

This brief inflationary episode sounds innocuous but it can solve many longstanding cosmological problems. A past period of accelerated expansion enables us to understand why our visible universe is expanding so close to the critical divide that separates open and closed universes. The fact that we are still so close to this divide, after about 15 billion years worth of expansion, is quite fantastic. Since any deviation from lying precisely on the critical divide grows steadily with the passage of time, the expansion must have begun extraordinarily close to the divide in order to remain so close today – so close that we still do not know on which side of the divide we lie. But the tendency of the expansion to veer away from the critical divide is just another consequence of the attractiveness of the gravitational force. But if gravity is repulsive and the expansion accelerates, it will drive the expansion ever closer to the critical divide. If inflation lasted for long enough – from 10^-35 s to 10^-33 s is enough – then it can explain why our visible universe is still so close to the critical divide.

Another by-product of a short bout of cosmic acceleration is that any large irregularities in the density of the universe get ironed out and the expansion very quickly goes at the same rate in every direction, just as we see today. This explains a property of the expansion of the universe that has always struck cosmologists as mysterious and unlikely – because there are so many more ways for the universe to expand at different rates in different directions. If inflation occurred, the whole of our visible universe can arise from the expansion of a region that is small enough for light signals to cross at very early times (see figure 4).

Any irregularities get ironed out very quickly in this universe. In the old, non-inflationary Big Bang theory the situation was very different. Our visible part of the universe had to emerge from a region vastly bigger than any that light rays could smooth out. It was therefore a complete mystery why our visible universe looks so similar in every direction on the sky to within one part in 100 000 – as observed.

In reality, the tiny region that grew into our visible universe could not have started out perfectly smooth. That is impossible. There must always be some tiny level of quantum statistical fluctuation present. Remarkably, a period of inflation stretches these fluctuations to very large astronomical scales, where they appear to have been seen by the COBE satellite. In the next few months they will be subjected to minute scrutiny by another satellite (MAP) that was launched in July 2001. If inflation occurred, the signals it receives should have very particular forms. So far, the data taken by COBE is in very good agreement with the predictions, but the really decisive features of the observable signal appear on angular scales too small for COBE to have resolved. The new satellite observations expected to be made by MAP and, later, by the Planck Surveyor (scheduled for launch in 2007), aided by increasingly accurate observations of smaller portions of sky from the Earth’s surface, will decide this question experimentally. In figure 5 we show a spectacular construction of what the microwave sky looks like from the Earth’s South Pole. The Boomerang team has recently made new observations of the microwave temperature fluctuations (see the Boomerang Project website at www.physics.ucsb.edu/~boomerang) from a balloon over a small patch of sky at much finer angular resolution than was possible with COBE.

In figure 6 we show a typical prediction of an inflationary universe model for the form of the fluctuation variation with angular scale, together with the observational data taken by Boomerang and other instruments near the Earth’s surface.  Satellite observations will ultimately reduce the experimental uncertainties so that they are smaller than the thickness of the theoretical curve on this plot and provide a powerful test of particular inflationary cosmological models of the very early universe. It is remarkable that these observations are providing us with a direct experimental probe of events that occurred when the universe was perhaps only about 10^-35 s old.
 

Eternal and chaotic inflation

Beyond the boundary of the little patch of the early universe that inflated to encompass the whole of our visible universe lie many (perhaps infinitely many) other such causally linked patches that can all undergo varying amounts of inflation to produce extended regions of our universe that lie beyond our visible horizon today. This leads us to expect that our universe possesses a complex spatial structure and the conditions that we can see within our visible horizon, about 15 billion light years away, are unlikely to be typical of those far beyond it. This complicated picture is usually termed “chaotic inflation” (Barrow and Tipler 1986, Linde 1994), see figure 7.

It has always been appreciated that the universe might have a different structure beyond our visible horizon. However, prior to the investigation of inflationary universe models this was always regarded as an overly positivistic possibility, often mooted by pessimistic philosophers, but which had no positive evidence in its favor. The situation has changed: the chaotic inflationary universe model gives a real reason to expect that the geography of the universe beyond our horizon differs from that in the visible part of the universe.
 
It was then realized by Alex Vilenkin and Andre Linde that the situation is probably even more complicated. If a region inflates then it generally creates within itself, on minute length scales, the conditions for further inflation to occur from many of its parts. This process can continue into the infinite future, with inflated regions producing further subregions that inflate, and so on ad infinitum. The process has no end. It has been called the “eternal” or “self-reproducing” inflationary universe (Linde 1994), figure 8. As yet, it is not known whether it need have a beginning.

 

How likely is it that a large life-supporting piece of the universe such as the region we can see arises in this eternal process? So far, nobody knows. The problem of defining unambiguously what is meant by probability in this process remains an unsolved problem.

The origami of the universe

The phenomenon of inflation is expected to occur when the universe is very young, just about 10^-35 s old. Such small times seem bizarre. Clearly, anthropomorphic units like “seconds” were not designed for cosmological problems. There are other humanly devised measures of time that might help alleviate the failure of our imaginations, but they would still fail to give a feeling that we had got the right superhuman perspective on cosmic time. Fortunately, there is a measure of time that is intrinsically defined by the forces of Nature that enables us to create a better perspective. In 1870 an Irish physicist, George Johnstone Stoney (also famous for both naming and predicting the value of the charge on an electron, see Barrow 1983, and Barrow and Tipler 1986 chapter 4), realized that three of the constants of Nature, e, G and c, could be combined to create units of mass, length and time that were independent of human standards. Thirty years later, Max Planck rediscovered this idea and created “natural units” using the constants of Nature: h, c and G (Barrow 2002). The resulting Planck– Stoney units of length, L_pl, and time, T_pl , are the only quantities with units of length and time that can be made from these fundamental constants which govern quantum, relativistic and gravitational phenomena. They are:

L_pl= (Gh/c³ )^1/2 =4.1.10^-33 cm

T_pl = (Gh/c³)^1/2 =1.3.10^-43 s

Theses scales of distance and time mark the boundaries, below which our current theories of gravity and quantum reality fail. They must be merged to create a new theory of quantum gravity. In effect, at times earlier than 10^-43 s the entire universe is dominated by quantum mechanical uncertainty. No-one knows what the structure of space will be like on scales smaller than L_pl , perhaps knotted or interconnected in some complicated way. However, it is fortunate that this problem only matters well before we expect inflation to occur.

In these natural units the visible universe is now 10⁶⁰ Planck times old and 10⁶⁰ times the Planck length in size. This is an objective way of saying that the universe is big and old without recourse to comparisons with human measuring artefacts. One way of looking at what inflation has done for the universe is to regard the Planck length as the natural size for a space under the influence of gravitational forces. Inflation can make the universe become much bigger, in our case 10⁶⁰ times bigger.

These numbers are still very large and it may be helpful to bring them closer to the imaginable in the following way. Suppose we take a piece of A4 paper and fold it in half, then in half again. You may be surprised to find that you can’t fold it more than seven times. Halving moves very quickly. If you could have folded the paper in half 30 times it would already be the size of a single atom; fold it 47 times and you are smaller than an atomic nucleus; fold it 114 times (a lot but not unimaginable) and you are down to the Planck length where quantum gravity (and quantum origami) rules. To make the link with the scale of the whole visible universe, imagine doubling the size of the A4 paper 90 times and it is about 10²⁷ cm in size. Just 204 paper-foldings divides the smallest and the largest dimensions of space in the physical universe.

What happens at the Planck scale?

The Planck scale is the final frontier for cosmologists at present. If we try to reconstruct the state of the universe earlier than the Planck time then we encounter an environment where no known laws apply for sure. The entire universe is beset by quantum uncertainty. Of course, this does not stop anyone from trying and there are many speculative scenarios that attempt to unravel the complexities of the Planck epoch and discover some residue of that era that might be observable today. We find mathematical studies of how the universe might have emerged quantum mechanically from some suitably defined state or greater simplicity, or even of “nothing”. One of the stimuli for such investigations is the feature that the energy of the universe is zero (Einstein’s equations ensure that the negative potential energies of attraction between all masses exactly cancel out the positive contributions from their masses and motions). New cosmologies have been proposed in which the expanding universe is a consequence of colliding sheets (“branes”) of energy. These ideas entail some aspects of the older models of “bouncing” universes that undergo a sequence of expanding and contracting phases like a bouncing ball. But yet more radical possibilities should be taken seriously. The familiar distinction between space and time should not be assumed to survive the Planck epoch, nor indeed should the simple picture of a fixed number of dimensions to space and time. These dimensions may change, or even cease to have a clear meaning at the Planck time. The most intensively studied superstring theories, and their successor M-theory, predict that there are more dimensions of space than the three with which we are familiar.

Extra dimensions

During his early career, the great German philosopher Immanuel Kant was more interested in science than in philosophy. He was a great admirer of Newton and his laws of gravity and motion and set himself to understanding them in different ways and to applying them to astronomical problems like the origin of the solar system. Kant’s most imaginative idea, sparked by Newton’s work, was to pose the question “Why does space have three dimensions?” (Handyside 1929). Kant had noticed a profound thing: that Newton’s famous inverse-square law of gravity was intimately connected with the fact that space has three dimensions. If space had four dimensions then there would be an inverse-cube law, if it had 100 dimensions there would be an inverse 99th power law of gravity. In general, an Ndimensional world exhibits a force law for gravity and electromagnetism that falls off as the (N–1)st power of distance. This is why we see inverse-square force laws in Nature.

The nature of universes with different dimensions of both space and time has been explored by a number of scientists (Barrow 1983). We can assume that the laws of Nature keep the same forms but permit the numbers of dimensions of space and time to range freely over all possibilities. The results are summarized (Tegmark 1998) in figure 9.

The chequer-board of all possibilities can be whittled down dramatically by the imposition of a small number of reasonable requirements that seem likely to be necessary for information processing and “life” to exist. If we want the future to be determined by the present then we eliminate all those regions of the board marked “unpredictable”. If we want stable atoms to exist along with stable orbits of bodies (planets) around stars then we cut out the strips marked “unstable”. Eliminating worlds in which there is only faster-than-light signaling we are left with our own world of 3+1 dimensions of space plus time along with very simple worlds that have 2+1, 1+1, and 1+2 dimensions of space plus time. Such worlds have no gravitational fields and are usually thought to be too simple to contain living things. Worlds with more than one time are hard to imagine and appear to offer many more possibilities. Alas, they seem to offer so many possibilities for happenings that the elementary particles of matter are far less stable than in worlds with a single time dimension. Protons can decay easily into neutrons, positrons and neutrinos and electrons can decay into neutrons, antiprotons and neutrinos. The overall effect of extra time dimensions is to make complex structures highly unstable unless they can exist at extremely low temperatures (Dorling 1969, Yndurain 1991).

Worlds with more than one time dimension do not allow the future to be predicted from the present. In this sense they are rather like worlds with no time dimension. A complex organized system, like that needed for life, would not be able to use the information gleaned from its environment to inform its future behaviour. It would remain simple, too simple to evolve.

The direct anthropic link between the number of dimensions of space and the existence of living observers was first made by the English cosmologist Gerald Whitrow in 1955. Asking the question “Why do we observe the universe to possess three dimensions?”, he sought to provide a new type of answer (Whitrow 1955, 1959), by arguing that thinking observers could only exist in three-dimensional worlds. Indeed, he suggested that it would be possible to deduce the dimensionality of world from the fact that we, or another form of intelligent life, exist. Whitrow’s approach is the first modern application of what would now be called an Anthropic Principle.

String theories are the only current theories of physics that do not lead to internal contradictions or to predictions that measurable quantities have infinite values when gravity is merged with the other forces of Nature. Yet these theories appear to require the universe to have many more dimensions of space than the three that we habitually experience. Since we are able to see only three dimensions we must conclude either that these theories are wrong, that dimensions can be something other than what we are used to thinking them to be, or that lots of dimensions of space are hiding somewhere.

While either of the first two options might turn out to be the case, it is generally assumed that the third provides the answer to the conundrum. Some process must be found that allows three (and only three) of the total number of dimensions of space to grow very large while the rest remain trapped at the Planck scale of size, where their effects are imperceptible to us. The conundrum is how three of them have become so much bigger – 10⁶⁰ times bigger – than the Planck size. What is required is a process that leads to the inflation of only three of the dimensions. At present no such selective process is known. It might be random in character, so that its choice of three large dimensions was not programmed into the laws of physics. Alternatively, there might be a deep reason why three and only three dimensions can inflate.

Putting the mystery of the selective inflation process to one side, we see that we are confronted with a major uncertainty. The true constants of Nature, and the forms of the laws of Nature, are really framed in more dimensions than three. The quantities that we call the constants of physics are just three-dimensional shadows thrown by the true constants. Remarkably, if the extra dimensions exist and change their size by expanding as our three-dimensional part of the universe does, then this would be revealed by a change in our “constants” of Nature at exactly the same rate (Marciano 1984, Barrow 1987, 2002).

One other escape from the consequences of extra dimensions and variations in constants that are seen to be constant to very high precision is currently being explored in great detail. Suppose only the gravitational force “sees” and influences all the dimensions of space. The other forces – electromagnetism, radioactivity and nuclear – only act in three of the dimensions (the “braneworld”) because they derive from strings whose endpoints are fixed on the brane surface. This braneworld picture shows why gravity is so much weaker than the other forces of Nature.

Changing constants

The realization that the constants of Nature we observe in three-dimensional space may not be fundamental, or constant, has renewed interest in testing their constancy by high-precision observations. During the last two years John Webb, Michael Murphy, Victor Flambaum, Vladimir Dzuba, Chris Churchill, Jason Prochaska, ArtWolfe and I have applied a new technique to analyse absorption spectra from distant quasars. We look at the separation between lines caused by the absorption of quasar light by different chemical elements in clouds of dust in between the quasar and us. These separations depend sensitively on the value of a particular constant of Nature, the fine-structure constant, α, at the redshift where the absorption occurs. By comparing with their separations here and now in the laboratory we have a probe of whether α can have altered over 12 billion years. This method is more than 500 times more sensitive than any other experimental probe of α and exploits the fact that a change in α affects separations between relativistic spectral lines in different species in very distinctive ways. A small decrease in α in the past will cause some separations between lines to increase and others to decrease. By using computational solutions of the equations of atomic structure, we can determine the shifts in line spacings that would result from tiny changes in α and find the shift, ∆α, that best fits the observed line separations. This method, which we call the many multiplet (or MM) method, is far more sensitive than the other astronomical methods. It has now been applied to observations of 147 quasars, looking at separations between their magnesium, iron, nickel, chromium, zinc and aluminium lines.

The results gathered and analyzed over two years have proved to be unexpected and potentially far-reaching. We find a persistent and significant difference in the separation of spectral lines at high redshift compared to the separation of the same lines when measured in the laboratory. The complicated fingerprint of shifts matches that expected if the value of the fine-structure constant was smaller by about seven parts in a million at the time when the absorption lines were formed. If we combine all the results then the overall pattern of variation that results (Webb et al. 2001, Murphy et al. 2001) is shown in figure 10.

If we take the observations of sources lying between redshifts of z = 0.5–3.5 as a whole, the observed shift is

∆α/α≡[α(z) – α(now)] / α(now) = –0.72 ± 0.18 .10^-5

A change in the fine-structure constant of this magnitude might have had adverse consequences 1.8 billion years ago (equivalent to a redshift of about 0.1 on Earth). We have geochemical data to show that a natural nuclear “reactor” ran intermittently below the Earth’s surface in Oklo, a region of Gabon in West Africa (Barrow 2002). These natural reactions only occurred because of a series of remarkable geological and nuclear coincidences.

A particular nuclear energy level that determines the probability of neutron capture by samarium must have remained the same to high precision between the operation of the natural reactor and the present. This energy level depends on the value of the constant α: the Oklo events imply ∆α/α<10^-7 when the reactor ran (Fujii et al. 2000). However, whereas Oklo limits changes in α about 2 billion years ago, the quasar observations span the range from about 3 to 12 billion years ago (Sandvik et al. 2002). Simple theories that include varying α are consistent with both limits because the variations cease when the universal expansion starts to accelerate at z ≈ 0.5–0.7 (see figure 11).

Before that it is predicted to increase slowly, as the logarithm of time, back to when the universe was about 300 000 years old, and to be constant before that (as shown in figure 12).

More important we find that if we fit the one free defining parameter in the varying-α theory so as to fit the quasar data as well as possible, it predicts that we should observe a violation of Einstein’s weak equivalence principle (that masses of different composition should fall with the same acceleration under gravity in a vacuum) at a level of one part in 10¹³. Existing observations place an upper limit of a part in 10¹² on any such violation, so a small increase in sensitivity, well within the reach of future space-based observations, could offer a critical independent test of the astronomical evidence for varying α.