CHRISTMAS LECTURE: The beginning and the end of the universe

Joint Meeting with the William Herschel Society

Prof. Sir Martin Rees, Astronomer Royal and Royal Society Research Professor at Cambridge University, on 14 December 2001

Professor Sir Martin Rees won the 2001 Cosmology Prize when the following Citation was written:

"Sir Martin Rees, Astronomer Royal and Royal Society Research Professor at Cambridge University, is renowned for his extraordinary intuition in unravelling the complexities of the universe. He has been a leader in the quest to understand the physical processes near black holes and is responsible for major advances in our understanding of the cosmic background radiation, quasars, gamma-ray bursts, and galaxy formation. He has contributed to almost every area of cosmology and astrophysics and has been an inspiring leader, eloquent spokesperson, and patient guide for astronomers all over the world. Through his public speaking and writing he has made the Universe a more familiar place for everyone".

Sir Martin was introduced by Victor Suchar, who organised the event. The lecture was illustrated with a large number of slides and followed by questions, which the speaker answered fully. At the end of his presentation a Vote of Thanks was proposed on behalf of both organisations by Professor Francis Ring, Chairman of the William Herschel Society.

Instead of an abstract of the lecture he presented, Sir Martin Rees has supplied a copy of a paper on the same subject which was published recently in "The Age of the Earth: from 4004BC to AD2002", CLE Lewis & SJ Knell (eds.), a Special Publication (190, 275-283, 0303-8719/01/$15.00), © by The Geological Society of London 2001 with permission to re-print it.

 

Understanding the beginning and the end of the universe

 

Abstract: This paper attempts to set the Earth in a cosmic perspective. It discusses the Sun's life cycle
in the context of stellar evolution, and the ideas of stellar nucleosynthesis, as an explanation of the origin of the atoms on the Earth. Current ideas on how planetary systems form are mentioned, along with data on recently discovered planets around other stars. The origin of matter itself can be traced back to a `Big Bang' corroboration of this model comes from the microwave background and from observed helium and deuterium abundances. There is now a concordance between stellar ages and the cosmic evolutionary timescale inferred from cosmology, from which we derive an age for the universe. Recent progress brings into focus a new set of questions about the ultra-early universe. Until these can be answered, it will remain a mystery why the universe is expanding in the observed fashion, and why it contains the measured mix of atoms, radiation and dark matter.

*****

Whilst this planet has been cycling on according to the fixed law of gravity, from so simple a beginning, forms most wonderful ...have been and are being evolved.

These are the famous closing words of Darwin's On the Origin of Species, but astronomers aim to go back before his `simple beginning', to set our entire Earth and Solar system in a broader context, stretching back to the birth of our galaxy, perhaps even to the initial instants of a `Big Bang' that set our entire universe expanding. Darwin guessed that it would have required hundreds of millions of years to have transformed primordial life (formed, he surmised, in a `warm little pond') into the amazing varieties of creatures that crawl, swim or fly on Earth. And this concept did not overly concern him, because such timespans had already been invoked by geologists to account for the laying down of rocks and moulding of the Earth's surface features.

Other contributors to this volume (Dalrymple 2001; Lewis 2001; Shipley 2001) have described how Kelvin estimated the Earth's age. His inferences about the age of the Sun were actually rather more firmly based than those about the Earth: if the gravitational energy released by its continuing contraction was supplying the heat radiating away, it would deflate in ten million years. Kelvin's views carried great weight. But it was perhaps fortunate for his reputation that he included an escape clause: his conclusion regarding the age of the Sun only held good, he said, provided that there was no other power source `prepared in the storehouse of creation' (Thomson 1862, p.393).

As was realised in the 1930s, fusion of hydrogen is sufficient to sustain the Sun for ten billion years. Our knowledge of atomic and nuclear physics is now sufficient to give us a (broadly uncontroversial) quantitative picture of the Sun's life cycle. The proto-Sun condensed from a cloud of diffuse interstellar gas. Gravity pulled it together until its centre was squeezed hot enough to trigger nuclear fusion of hydrogen into helium at a sufficient rate to balance the heat shining from its surface. (Any deuterium in the original cloud would have been burnt at an earlier stage in the contraction.) Less than half the Sun's central hydrogen has so far been used up: it is already 4.5 billion years old, but will keep shining for a further 5 billion years. It will then swell up to become a red giant, large and bright enough to engulf the inner planets, and to vaporise all life on Earth. During this `red giant' phase, lasting some five hundred million years, hydrogen will continue to burn in a shell around the helium core. Next, the Sun will undergo a more rapid convulsion, triggered by the onset of helium fusion in its core. This blows off some outer layers - about a quarter of the Sun's mass altogether. The residue will become a white dwarf - a dense `stellar cinder' no larger than the Earth, which will shine with a bluish glow, no brighter than today's full Moon, on whatever remains of the solar system.

Our Sun has more time ahead than has so far elapsed; as explained later, our entire universe could have an infinite future ahead of it. So we may still be near Darwin's `simple beginning': if life is not prematurely snuffed out, our remote progeny will surely -in the aeons that lie ahead -spread far beyond this planet. Even if life is now unique to the Earth, there is time enough for it to spread through the entire galaxy, and even beyond.

The structure and life cycle can be computed for a star of any mass. The output of such calculations allows us to infer the ages of star clusters, which contain a population of coeval stars of different masses. The key idea is that heavier stars use up their core hydrogen fuel, and `burn out', more quickly than lower-mass stars. The older a system is, the fainter (and lower-mass) will be the brightest stars that are still in the hydrogen-burning phase. Particularly interesting in this regard are the so-called `globular clusters' - each a swarm of up to a million stars, of different sizes, held together by their mutual gravity - which are believed to be the oldest stellar systems of all. The uncertainties in the age estimates stem partly from the theoretical models themselves, but also from the difficulty of inferring stellar masses from observed brightness and colours. Estimated ages are up to 13 billion years, with, however, an uncertainty of at least 10%. Such estimates are of course crucial to cosmology, because it would be embarrassing if the inferred age of the entire universe (in other words the time since the Big Bang) were not comfortably higher than the age of the oldest stars. As I shall comment later, there now seems no such paradox.

Not everything happens slowly. Massive stars
end their lives violently by exploding as super-novae. The closest supernova of the twentieth century flared up in February 1987. Its subsequent fading has been followed by all the techniques of modern astronomy. Theorists were given a chance to check the elaborate computer calculations they had developed over the previous decade. In about 1000 years its remnant will look like the Crab Nebula - the expanding debris from an explosion recorded by Chinese astronomers in 1054AD; in a few thousand more years, it will have merged into the general interstellar medium. Supernovae fascinate astronomers, but why should Earth-bound scientists - geologists in particular - care about stellar explosions thousands of light years away? The answer, of course, is that supernovae made the atoms that the Earth is made of: without them we would not be here. On Earth, for every ten atoms of carbon, there are about 20 of oxygen and five each of nitrogen and iron. But gold is a million times rarer than oxygen; platinum and mercury are rarer still. These exploding stars suggest the reason why (Salpeter 1999).

Stars more than ten times heavier than the Sun use up their central hydrogen hundreds of times quicker than the Sun does - they shine much brighter in consequence. Gravity then squeezes them further, and the centres get still hotter, until helium atoms can themselves stick together to make the nuclei of heavier atoms. A kind of `onion skin' structure develops: a layer of carbon surrounds one of oxygen, which in turn surrounds a layer of silicon. The hotter inner layers have been transmuted further up the periodic table and surround a core that is mainly iron. When their fuel has all been consumed, big stars face a crisis. A catastrophic infall compresses the stellar core to neutron densities, triggering a colossal explosion - a supernova.

The outer layers of a star, by the time a supernova explosion blows them off, contain the outcome of all the nuclear alchemy that kept it shining over its entire lifetime. Elements beyond the Fe peak can be built up during the explosion itself. Work over the last 40 years - taking account of different types of stars, different nuclear reactions - has shown that the calculated `mix' of atoms is gratifyingly close to the proportions now observed in our solar system. This story is well authenticated by detailed modelling of the expected relative abundances of elements and isotopes, and also by spectroscopic evidence from the oldest stars (which contain less processed material). It is also found that the abundances are higher in gaseous environments like the galactic centre, where reprocessing would be fast, and lower in locations like the Magellanic Clouds where it is slower .

Our galaxy is like an ecosystem, recycling gas through successive generations of stars, gradually building up the entire periodic table. Before our Sun even formed, several generations of fast-burning heavy stars could have been through their entire life cycles, transmuting pristine hydrogen into the basic building blocks of life - carbon, oxygen, iron and the rest. We are literally the ashes of long-dead stars.

Planets around other stars?

One fascinating question, of course, is whether other worlds are orbiting other stars. For a long time astronomers have suspected planetary systems to be common, because proto-stars, as they contract from rotating clouds, spin off around them discs of dusty gas. These have now been seen in the Orion Nebula and else-where. In such discs, dust particles would stick together to make rock-sized lumps, which can in turn merge to make planets (the volatiles being lost from the inner planets, but not from the outer giant planets). Evidence for actual planets orbiting other ordinary stars is harder to find, but it came in 1995. In that year, two Swiss astronomers, Michel Mayor and Didier Queloz, found that the Doppler shift of 51 Pegasi, a nearby star, resembling our Sun, was varying sinusoidally by 50 m/s. They inferred that a planet weighing a thousandth as much was circling it at 50 km/s, causing the star to pivot around the combined centre of mass. Five years later, similar periodic wobbles in other stars have been detected; the number of inferred planets now exceeds fifty.

Several research groups have contributed to that total, Marcy & Butler (2000) in California being the `champions'. Some systems have two or even three planets. But the inferred planets are all big ones - like Jupiter or Saturn. These may be the largest members of other planetary systems like our own, but Earth-like planets would be hundred times harder to detect.

Planets on which life could evolve, as it did here on Earth, must be rather special. Their gravity must pull strongly enough to prevent an atmosphere from evaporating into space; they must be neither too hot nor too cold, and therefore the right distance from a long-lived and stable star. Most of Marcy & Butler's systems are not propitious - they contain Jupiters on eccentric orbits close to the star, which would preclude any stable orbit for a planet in the zone where water neither always freezes nor always boils. There is still theoretical dispute about how these (presumably hydrogen-rich) planets achieved orbits so close in. It is possible that the typical system formed with two or three `Jupiters'. Interactions between them would expel one, leaving the others on eccentric orbits. Maybe our solar system is unusual in having only one Jupiter. But planetary systems are (we believe) so common in our galaxy that Earth-like planets should be numbered in millions A search for Earth-like planets
is now a main thrust of NASA's programme (NASA = the National Aeronautics and Space Administration, USA). It is a long-term technical challenge requiring large telescope arrays in space - but it is not as crazy as it sounds. Once a candidate had been identified, several things could be learnt about it. Suppose an astronomer forty light years away had detected our Earth -it would be, in Carl Sagan's phrase, a `pale blue dot', seeming very close to a star (our Sun) that outshines it many million times. If Earth could be seen at all, its light could be analysed, which would reveal that it had been transformed (and oxygenated) by a biosphere. The shade of blue would be slightly different, depending on whether ocean or land mass was facing us. Distant astronomers could therefore, by repeated observation, infer the Earth was spinning, and learn the length of its day, and even infer something of its topography and climate.

The concept of a `plurality of inhabited worlds' is still the province of speculative thinkers, as it has been through the ages. The year 2000 marks the fourth centenary of the death of Giordano Bruno, burnt at the stake, in Rome for his belief that:

There are countless constellations, suns and planets; we see only the suns because they give light; the planets remain invisible, for they are small and dark. There are also numberless earths circling around their suns, no worse and no less than this globe of ours.

Only within the last five years has this conjecture been vindicated. But Bruno went on to say:

For no reasonable mind can assume that heavenly bodies which may be far more magnificent than ours would not bear upon them creatures similar or even superior to those upon our human Earth (Bruno 1584).

Here we are still in the speculative realm. But, of course, what motivates NASA and the American public, is whether there is life on any of the other Earths. Even in a propitious environment, what is the chance that `simple' organisms emerge? Even when they do what is the chance they evolve into something that can be called intelligent? These questions are for biologists - they are too difficult for astronomers. There seems no consensus among the experts. Intelligent life could be `natural'; or it could have involved a chain of accidents so surpassingly rare that nothing remotely like it has happened anywhere else in our galaxy.

 

The extragalactic universe: back towards the beginning

 

Let us now get back to the (relative) simplicity of the inanimate world. I have mentioned briefly how the atoms of the periodic table are made - that we are the `nuclear waste' from the fuel that makes stars shine. But where did the original hydrogen come from? To answer this question, we must extend our horizons to the extragalactic realm. Our galaxy, with its hundred billion stars, is similar to millions of others visible with large telescopes. Andromeda, the nearest big galaxy to our own, lies about two million light years away. Its constituent stars are orbiting in a disc, seen obliquely. In others, like the Sombrero galaxy, ten billion stars are swarming around in more random directions, each feeling the gravitational pull of all the others.

The nearest few thousand galaxies - those out to about 300 million light years -have been mapped out in depth. They are irregularly distributed into clusters and superclusters. Are there, you may ask, clusters of clusters of clusters ad infinitum? It does not appear so. Deeper surveys show a smoother distribution: our universe is not a fractal. If it were, we would see equally conspicuous clumps, on ever-larger scales, however deep into space we probed. But even the biggest superclusters are still small in a comparison with the horizon that powerful telescopes can reach. So we can define the average `smoothed-out' properties of our observ- able universe. An analogy may be helpful here. If you are in the middle of an ocean, you may be surrounded by a complex pattern of waves, but even the longest-wavelength ocean swells are small compared to the horizon distance; you can therefore define `average' properties of the waves. In contrast, if you are on land, in mountainous terrain, a single peak may dominate the entire view, and it makes less sense to define averages. Cosmology has proved a tractable subject because, in terms of this analogy, our universe resembles a seascape rather than a mountain landscape.

The overall motions in our universe are simple too. Distant galaxies recede from us with a speed proportional to their distance, as though they all started off packed together 10-15 billion years ago. But this does not imply we are in a special location. Suppose that all clusters of galaxies were joined by rods, which all lengthened at a rate proportional to how long they were. Then any two clusters would recede from each other with a speed proportional to their distance. That is what seems to be happening in our universe: there is no preferred centre, and an observer on any cluster would see an isotropic expansion around them.

What we actually see is modified by the fact that light takes a long time to reach us from distant places. As we probe deeper into space, towards our horizon, we see the universe as it was when it was younger and more closely packed. And we can now see very far back. Some amazing pictures taken with the Hubble Space Telescope each show a small patch of sky, less than a hundredth of the area covered by a full Moon. Viewed through a moderate-sized telescope, these patches would look completely blank. But these ultra-sensitive long
exposures reveal many hundreds of faint smudges of light - a billion times fainter than any star that can be seen with the unaided eye. But each is an entire galaxy, thousands of light years across, which appears so small and faint because of its huge distance.

A huge span of time separates us from these remote galaxies. They are being viewed at the time when they were only recently formed, before they settled down into steadily spinning `pinwheels' like Andromeda. Some consist mainly of glowing diffuse gas that has yet to condense into stars. When we look at Andromeda, we sometimes wonder if there may be other beings looking back at us. Maybe there are. But surely not on these remote galaxies. Their stars have not had time to manufacture the chemical elements. They would not yet harbour planets, and presumably no life. Astronomers can actually see the remote past. But what about still more remote epochs, before any galaxies had formed?

Georges Lemaitre and George Gamow pioneered the idea that everything had `exploded' from an initial dense state, which Lemaitre called the `primeval atom', and Gamow the `ylem'. Neither of these names have stuck: we now talk about the `Big Bang', a phrase introduced by Fred Hoyle as an insulting description of a theory he disliked. In 1948 Hoyle had developed, in collaboration with Thomas Gold and Hermann Bondi, the concept of a steady-state universe (Brush 2001): new atoms (and new galaxies) were postulated to be continuously created, so that, despite the expansion, the cosmos persisted with constant mean density in a statistically unchanging state.

There was boisterous and inconclusive debate in the 1950s (for more on this see Brush 2001), centred on whether the statistics of the `radio galaxies' were compatible with a steady state, but clinching evidence for a Big Bang came in 1965. Intergalactic space is not completely cold. It is pervaded by weak microwaves, which have now been measured by the COBE satellite at many different wavelengths to a precision of one part in 10,000. This spectrum is just what you would expect if these microwaves are indeed an `afterglow' of a pre-galactic era when the entire universe was hot, dense and opaque. The expansion has cooled and diluted the radiation, and stretched its wavelength. But this primordial heat is still around - it fills the Universe and has nowhere else to go!

And there is another `fossil' in the universe - helium. When the entire universe was squeezed hotter than a star, there would have been nuclear reactions, but the temperature is only that high for the first three minutes - not enough time (fortunately) to convert everything into iron. (However, if that had happened, stars could still have formed, but they would exist only for Kelvin's timescale mentioned earlier, and there would be no hydrogen, carbon, oxygen and silicon to make the Earth.) During the expansion that immediately followed the Big Bang, reactions between protons and neutrons would have resulted in 23% of the material emerging as helium. This is gratifying because the theory of stellar nucleogenesis, which accounted so well for the build-up of most of the periodic table was hard-pressed to explain why helium was much more uniform in its abundance than the heavier elements. The only other nucleus that is a relic of the Big Bang (apart, maybe, from lithium) is deuterium. This is an intermediate product in the primordial fusion of helium: the predicted deuterium abundance of a few parts in a hundred thousand is concordant with observations. Deuterium is destroyed in the course of stellar evolution, so its attribution to the Big Bang solves a long-standing problem.

The extrapolation back to the stage when the universe had been expanding for a few seconds (when the helium formed) deserves, I think, to be taken as seriously as anything that geologists or palaeontologists tell us about the early history of our Earth. Their inferences are just as indirect (and less quantitative). Moreover, there are several discoveries that might have been made, which would have invalidated the hypothesis, and which have not been made. For instance:

(i) the astronomers might have discovered an object with helium abundance zero, or at least much less than 23%;

(ii) the microwave background was first observed, with poor spectral accuracy, in the 1960s. It might have turned out not to have a `black body spectrum';

(iii) according to the Big Bang theory, photons out-number baryons by a factor of about a billion. Moreover, in the first second of cosmlc expansion, photons would come into equilibrium with neutrinos. There would therefore be roughly as many neutrinos as photons (the number differs by a modest numerical factor, because neutrinos and photons obey different quantum statistics, and the photon density is boosted by electron-positron annihilation). If physicists had found, experimentally, that one species of (stable) neutrino had amass in the range 100 to 1,000,000 electron volts, then the total mass of all the predicted neutrinos would have `closed up' the universe on much less than its present scale.

It would be easy to lengthen this list. The crucial point, however, is that the Big Bang theory has lived dangerously for decades, and survived. I believe we should place 99% confidence in an extrapolation back to the stage when the universe was one second old and at a temperature of ten billion degrees kelvin. However, we have far less confidence about still earlier stages - the first tiny fraction of a second - and I will return to this later. But first let us briefly look forwards rather than backwards - as forecasters rather than fossil hunters.
Futurology

In about five billion years the Sun will die; and the Earth with it. At about the same time (give or take two billion years!) the Andromeda galaxy, already falling towards us, may crash into our own Milky Way. So will the universe go on expanding for ever? Or will the entire firmament eventually collapse to a `Big Crunch'?

The answer depends on how much the cosmic expansion is being decelerated by the gravitational pull that everything exerts on everything else. It is straightforward to calculate that the expansion can eventually be reversed if there are, on average, more than about five atoms in each cubic metre. That seems very little, but if all the galaxies were dismantled, and their constituent stars and gas spread uniformly through space, they would make an even emptier vacuum - one atom in every ten cubic metres - like one snow- flake in the entire volume of the Earth.

Such a concentration is fifty times less than the `critical density', and at first sight this seems to imply perpetual expansion, by a wide margin. But it is not so straightforward. Astronomers have discovered that galaxies, and even entire clusters of galaxies, would fly apart unless they were held together by the gravitational pull of about ten times more material than we actually see - this is the famous `dark matter' mystery .

One line of evidence for this dark matter comes from studying the orbits of stars and gas in the outlying parts of galaxies -far outside the region that gives most of the visible light. These orbits are surprisingly fast. It is as though we found that Pluto were orbiting the Sun as fast as the Earth is. Were that the case, we would need to postulate an invisible heavy `shell' outside the Earth's orbit but inside Pluto's, so that Pluto was `feeling' the inward gravitational pull of a larger mass. It seems that the luminous parts of galaxies are embedded in a swarm of invisible objects, five to ten times more extensive and contributing five to ten times more total mass. On a still larger scale, entire clusters of galaxies contain dark matter. This is revealed in several ways. One interesting line of evidence comes from gravitational lensing - the bending of light by gravity. This technique was first suggested in the 1930s by the Swiss-American astrophysicist Fritz Zwicky, but has only recently been observationally feasible.

Among the undoubted highlights of the discoveries made with the Hubble Space Telescope are high-resolution pictures of clusters of galaxies. A remarkable image of the cluster Abe1 12218, a billion light years away, shows many galaxies in the cluster. But the picture also reveals a lot of faint streaks and arcs: each is a remote galaxy, several times further away than the cluster itself, whose image is, as it were, viewed through a distorting lens. Just as a regular pattern on background wallpaper looks distorted when viewed through a curved sheet of glass, the gravity of the cluster of galaxies deflects the light rays passing through it. The visible galaxies in the cluster contain only a tenth as much material as is needed to produce these distorted images - evidence that clusters, as well as individual galaxies, contain ten times more mass than we see.

What could this dark matter be? It is embarrassing that 90% of the universe is unaccounted for! Most cosmologists believe the dark matter is mainly exotic particles left over from the Big Bang, If they are right, we have to take our cosmic modesty one stage further. We are used to the post-Copernican idea that we are not in a special place in the cosmos. But now even `particle chauvinism' has to go. We are not made of the dominant stuff in the universe. We, the stars, and the galaxies we see are just traces of `sediment' - almost a seeming after-thought - in a cosmos whose large-scale structure is dominated by particles of a quite different (and still unknown) kind. Checking this is perhaps the number-one problem in the whole subject.

Cosmologists denote the ratio of the actual density to the critical density by the Greek letter omega (W). There is certainly enough dark matter around galaxies to make W = 0.2 (remember that what we see is only 0.02). Until recently, we could not rule out several times this amount - comprising the full critical density, W = 1 -in the space between clusters of galaxies. But it now seems that, in total, atoms and dark matter contribute no more than about W = 0.3. The odds, therefore, favour perpetual expansion. The galaxies will fade, as their stars all die, and their material gets locked up in old white dwarfs, neutron stars and black holes. They will recede ever further away, at speeds that may diminish but never drop to zero. In fact, there is now tantalising evidence for an extra repulsion force that overwhelms gravity on cosmic scales - what Einstein called the cosmological constant, lambda (l). The expansion may actually accelerate! If it does, the forecast is an even emptier universe (see Schramm 1998). The American magazine Science rated this the most important discovery of 1998, in any field.

The issue of acceleration versus deceleration is important for another issue, the `age of the universe' - in other words, the time since the Big Bang. If expansion proceeded at an unchanging speed, this would be simply the `Hubble time' - the inverse of the Hubble constant, which gives the relation between recession speed and distance (for a further explanation of `Hubble time', see Brush 2001). The Hubble time is still uncertain at the 10% level, but current best estimates are in the range 13-14 billion years. However, if the universe were decelerating, the average expansion speed would
have been faster than the present speed, and the time since the Big Bang consequently shorter than the Hubble time. For example, the age of an `Einstein-de Sitter' universe, where the matter provides the full critical density (i.e. where W=1), is only two- thirds of the Hubble time. If we were in such a universe, there would be a serious discrepancy with the estimated ages (up to 13 billion years) of globular star clusters. However, in an accelerating universe, the time since the Big Bang can exceed the Hubble time. For the cosmological model which is now most favoured (where the `cosmical repulsion' is dominant, causing an acceleration, whereas at earlier times, when the matter was denser, there would have been deceleration) the `age' works out at a value close to the Hubble time. There therefore seems, taking account of the 10% errors in both the Hubble time and in stellar ages, a reassuring concordance between these estimates.

 

The ultra-early eras

 

So much for the long-range forecast. Let us now go back to the beginning. People sometimes wonder how our universe can have started off as a hot amorphous fireball and ended up intricately differentiated. Temperatures now range from blazing surfaces of stars (and their even hotter centres) to the night sky only three degrees kelvin above absolute zero. This may seem contrary to a hallowed principle of physics: the second law of thermodynamics. But it is actually a natural outcome of the workings of gravity.

Gravity renders the expanding universe unstable to the growth of structure, in the sense that even very slight initial irregularities would evolve into conspicuous density contrasts. Theorists can now follow a `virtual universe' in a computer. Slight fluctuations are `fed in' at the start of the simulation. The calculations can simulate a box containing a few thousand galaxies - large enough to be a fair sample of to our universe. As the box expands, regions slightly denser than average lag further and further behind. Eventually, gravitationally bound systems of dark matter would condense out, to become the `dark halos' of new galaxies. Within these halos, gas cools and condenses into stars, When stars have formed, the negative specific heat of gravitating systems drives things further from equilibrium. If the Sun's nuclear fuel were turned off, it would contract, just as Kelvin realised. But it would end up with a hotter centre than before: to provide an enhanced pressure to balance the stronger gravitational force, the centre must, after contraction, get hotter. When a star loses energy, it heats up.

The way slight initial irregularities in the cosmic fireball evolve into galaxies and clusters is in principle as predictable as the orbits of the planets, which have been understood since Newton's time. But to Newton, some features of the solar system were a mystery. Why were the planets `set up' with their orbits almost in the same plane, all circling the Sun the same way, whereas the comets were not? This is now well understood: the planets have aggregated from smaIler bodies within a disc that was `spun off' from the contracting proto-Sun. Indeed, we have pushed the barrier back from the beginning of the solar system to the first second of the Big Bang. But conceptually we are in no better shape than Newton was. He had to specify the initial trajectories of each planet. We have pushed the causal chain further back by several `links', but we still reach a stage when we are reduced to saying "things are as they are, because they were as they were".

Our calculations of cosmic structure need to specify, at some early time such as one second after the Big Bang, a few numbers:

i) The cosmic expansion rate;

ii) the proportions of ordinary atoms, dark matter and radiation in the universe;

(iii) the character of the fluctuations; and, of course,

(iv) the basic laws of physics.

 

Any explanation for these numbers must lie not just within the first second, but within the first tiny fraction of a second. What is the chance, then, of pushing the barrier back still further? The cosmic expansion rate presents a special mystery. The two eschatologies - perpetual expansion, or collapse to a `crunch' - seem very different. But our universe is still expanding after ten billion years. A universe that collapsed sooner would not have allowed time for stars to evolve, or even to form. On the other hand, if the expansion were too much faster, gravity would have been overwhelmed by kinetic energy and the clouds that developed into galaxies would have been unable to condense out. In Newtonian terms the initial potential and kinetic energies were very closely matched. How did this come about?

 

I was confident in tracing back to when the universe was a second old. The matter was no denser than air; conventional laboratory physics is applicable and is vindicated by the impressive evidence of the background radiation, helium, and so forth. But for the first trillionth of a second every particle would have had more energy than even CERN's new accelerator will reach (CERN = Organisation Europeene pour la Recherche Nucleaire). The further we extrapolate back, the less foothold we have in experiment.

But most cosmologists suspect that the uniformity and expansion rate is a legacy of some- thing remarkable that happened when everything was compressed in scale by 27 powers of ten (and hotter by a similar factor). The expansion would then have been exponentially accelerated, so that
an embryo universe could have inflated, homogenized and established the `fine-tuned' balance between gravitational and kinetic energy when it was only 10-38 seconds old (see Turner 2001 for a review). The seeds for galaxies and clusters could then have been tiny quantum fluctuations, imprinted when the entire universe was of microscopic size, and stretched by inflationary expansion.

This generic idea that our universe inflated from something microscopic is compellingly attractive. It looks like `something for nothing', but really is not. That is because our present vast universe may, in a sense, have zero net energy. Every atom has an energy because of its mass - Einstein's E = mc2. But it has a negative energy due to gravity - we, for instance, are in a state of lower energy on the Earth's surface than if we were up in space. And if we added up the negative potential energy we possess due to the gravitational field of everything else, it could cancel out our rest mass energy. Thus it does not, as it were, cost anything to expand the mass and energy in our universe.

Cosmologists sometimes loosely assert that the universe can essentially arise `from nothing'. But they should watch their language, especially when talking to philosophers. The physicist's vacuum is latent with particles and forces - it is a far richer construct than the philosopher's `nothing'. Physicists may, some day, be able to write down fundamental equations governing physical reality. But they will never tell us what `breathes fire' into the equations, and actualises them in a real cosmos.

I am uneasy about how cosmology is sometimes presented. The distinction is often blurred between things that are quite well established and those that are still speculative. I have tried to emphasise that as far back as one second after the Big Bang, I regard cosmology as having as firm a base as other historical sciences. But the ultra-early universe is more speculative, and I must offer a special health warning for mentioning it - and a redoubled warning before the brief remarks in the next section.

 

A multiverse?

 

In our universe, intricate complexity has un-folded from simple laws - we would not be here if it had not. But simple laws do not necessarily permit complex consequences - one could envisage a set of laws that precluded any emergent structures. To take an analogue, the Mandlebrot set, with its infinite depth of structure, is encoded by a short algorithm. But other algorithms, superficially similar, yield very boring patterns. Why is the physical `recipe' for our universe, in this analogy, like the Mandelbrot set?

As we have seen, our cosmos could not have evolved its present complexity if it were not expanding at a special rate. And there are other prerequisites for a complex cosmos. We can a readily imagine other alterations that would preclude complexity. For instance, if nuclear forces were a few per cent weaker, no atoms other than hydrogen would be stable. The residue of the Big Bang might be entirely dark matter - no ordinary atoms at all. Gravity could be so strong that any large organism would be crushed. Or the number of dimensions might even be different.

This apparent `fine tuning' could be just a brute fact, but I find another interpretation increasingly compelling: it is that many other universes actually exist. Most would be `still-born' because they collapse after a brief existence, or because the physical laws governing them are not rich enough to permit complex consequences. Only some would allow creatures like us to emerge. And we obviously find ourselves in one of that particular subset. The seemingly `designed' features of our universe need then occasion no surprise. If you go to a clothes shop with a large stock, you're not surprised to find one suit that fits. I have argued in a recent book (Rees 1999) that our universe may not be the only one. Some of the key numbers that characterise ours may take different values in others, which would then be sterile. But this is speculation and it may go the way of Kepler's numerology - he thought there were six planets, in orbits with definite geometrical ratios.

 

Conclusions

 

It is helpful to divide cosmic history into three parts.

Part 1 is the first millisecond, a brief but eventful era spanning forty decades of logarithmic time. This is the intellectual habitat of the high-energy theorist and the `inflationary' or quantum cosmologist. Here, there are uncertainties in the basic physics, which get more serious the further back we go, since we gradually lose our foothold in experiment. But the key features of our universe were imprinted during this era.

Part 2 runs from a millisecond to some millions of years: it is an era when cautious empiricists like myself feel more at home. The physics is well-known, and everything is still smoothly expanding. Theory is corroborated by quantitative evidence: the cosmic helium abundance, the background radiation, etc. Part 2 of cosmic history, though it lies in the remote past, is the easiest to understand. The tractability lasts only as long as the universe remains amorphous and structureless. When the first structures condense out, the first galaxies and stars form and light up - the era studied by traditional astronomers begins. We then witness complex manifestations of well-known basic laws. Gravity, gas dynamics and feedback processes from early stars combine to initiate the complexities around
us.

Part 3 is difficult for the same reason that geology and other environmental sciences are difficult. Edwin Hubble concluded his famous book The Realm of the Nebulae, with the words: `Only when empirical resources are exhausted do we reach the dreamy realm of speculation' (Hubble 1936). We still dream and speculate. But there has been astonishing empirical progress since Hubble's time. The last decade has been exceptional, and the crescendo of discovery seems set to continue. Large telescopes on the ground, and the instrument in space that bears Hubble's name, can now view 90% of cosmic history; other techniques can probe right back to the first few seconds of the `Big Bang'.

There are three great frontiers in science: the very big, the very small and the very complex. Cosmology involves them all. Cosmologists must pin down the basic numbers like the `density parameter' omega, and find what the dark matter is - I think there is a good chance of achieving this within five years. Second, theorists must elucidate the exotic physics of the very earliest stages, which entails a new synthesis between cosmos and microworld - it would be presumptuous for me to place bets here. But cosmology is also the grandest of the environmental sciences,and its third aim is to understand how a simple fireball evolved, over 10 to 15 billion years, into the complex cosmic habitat we find around us - how, on at least one planet around at least one star, creatures evolved able to wonder about it all. That is the challenge for the new millennium.

 

I am grateful to H. Huppert and G. Rhee for carefully reading a draft of this article.

 

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