The Early History of the Universe

Professor John Barrow

My aim today is to try to tell you something about the very early stages of the universe, as we understand them at present; to try to reconstruct the past history of the universe.  Usually one does this by going backwards in time, step by step, deeper into the past, until you seem to reach a point through which you cannot continue.  I am going to do the opposite - the contrary, if you like; I am going to start at the beginning and work forwards to the present.  Any type of reconstruction of the past history of the universe is always a slightly dodgy enterprise.  The famous remark that was made by a Russian historian some while ago applies also to cosmology: ‘As you change what you know about the present, it also alters some of your interpretation of what must have gone on in the past history of the universe.’

Talking about strange remarks, while I was in America recently there was a rather unusual great road sign down in the Deep South: ‘Big Bang Theory?  You’ve got to be kidding, God!’

Well, let us start not quite at the beginning, but at the earliest point where physicists think that they can talk sensibly about the conditions in the universe.  You will recall that the universe is expanding today, and so if we run the clock backwards in time, we should encounter conditions of ever-increasing temperature and density as we go to earlier and earlier moments.  If we just run backwards in that way, we would come to a halt; we would encounter a place where formerly the density was infinite and there was no earlier time that we could understand, only about 13.7 billion years ago.  That is very striking because you can find rocks on the Earth that are more than 4 billion years old, our galaxy is more than 10 billion years old, so you do not have to go back very much further in time before you seem to encounter what could be the beginning of everything.  So a question like ‘What was the universe like 20 billion years ago?’ does not have an answer.  It is a bit like asking ‘what colour is the number seven?’  It would be a sort of category mistake.

If we try to go backwards to this apparent beginning, there is a time when people start to talk seriously about what might be going on in the universe using the physics that we would like to know, and in some sense partially know.  That beginning occurs in a very particular moment of time.  What the moment characterises is the time when quantum theory is necessary to understand the force of gravity.

Quantum theory tells us that everything that we see that has mass and size and energy - has a sort of wave-like quality - and this wave-like quality is not a wave goodbye, as it were, or even a water wave; it is more like a crime wave – it is a wave of information.  If a crime takes place in your neighbourhood, we say that there is a crime wave perhaps hitting your neighbourhood.  What does that mean?  It means that a crime is more likely to be found to be committed in your neighbourhood, so a crime wave is a wave of information.  A quantum wave is like that as well.  It means if an electron wave passes through your laboratory, you are more likely to detect that entity that we call an electron in your detector. 

Well, back at a very particular time in the universe, this wave-like aspect of the universe has a size and extent which is bigger than the whole dimension of the universe over which light can travel.  So if you think of each object having a sort of wavelength, which defines the distance over which it is uncertain, because of quantum mechanical effects, then you start to worry when that size of quantum fuzziness becomes bigger than the actual size of an object.  Because that size of fuzziness is inversely proportional to a mass, for you and me, our wavelength of quantum fuzziness is absolutely microscopic. It is really tiny and is much, much smaller than ourselves.   So when we walk down the street, we do not have to worry about quantum fuzziness influencing our decision when to step off the kerb to cross the road.  But as objects get smaller and smaller, the quantum fuzziness extent gets bigger and bigger, and at this particularly outrageously small time in the past, the quantum fuzziness scale of the whole universe is bigger than its physical size.  That means that everything that you want to know about the universe and the forces that act upon it become dominated by this quantum fuzziness.  So far, we have ideas, like Super String Theory, about how you should arrive at a description of the universe in that state, but no theory of actually how it is implemented.

For this reason, people tend to think that all bets are off if you try to understand what is going on in the universe before this extraordinarily small time.  It is sometimes call the Planck time because Max Planck was the first person who derived it, although not for reasons that were anything to do with cosmology.  The reason he derived it is shown by displaying what the formula for it is.  It is a combination of 3 constants of nature: one, Newton’s Constant of Gravity; the speed of light to the power 5; and Planck’s Quantum Constant, which determines the scale of fuzziness attached to a particular mass.  If you combine them, multiply these two, divide by the 5th power, take the square root, then you get a quantity that has units of a time, and there is only one way to do that, and that is that way.  So there is something very fundamental about this time.  It is relativistic, it is gravitational, and it is quantum mechanical.  It is picked out by the constants of nature rather than by what happens to be a convenient time for us to measure – seconds, years, or something like that.  So this is the tick on which the universe time proceeds.  It is a fundamental time, and it has, corresponding to it, a fantastically high temperature of 10 to the 32 degrees Kelvin.  All the temperatures I mention will be in degrees Kelvin.  Zero degrees Kelvin, you will remember, is minus 273 Centigrade.

So, this is when the story starts to unfold, at this fantastically high temperature, and what you can imagine happening, as the temperature cools below that value, the force of gravity starts to become distinct from the other forces of nature, goes its own way, and we have a period where the other three forces, the strong, the weak and the electromagnetic, act as though they are a single force. 

What does the universe look like really at this time?  Nobody really knows.  At this time, the nature of space itself could be tangled and knotted.  We do NOT know if time would flow in an orderly and predictable way like it does today.  So a new theory of what happens at this time could change almost everything about our description of space, time, matter in the universe.

It is interesting to visualise some things about this time.  How big is the universe at that amazingly small time? Well, if you multiply the time by the speed of light, that would tell you how far a light wave would go in that time, and that gives you the corresponding length or size.  Again, it just depends on those 3 great constants of nature, and it has a tiny extent, 10 to the minus 33 of a centimetre.  If you want to know how big the universe is today in a way that is meaningful irrespective of our prejudices about length – feet, metres, miles or whatever – then the size of the universe today is about 10 to the power 60 of these Planck lengths, and its age is also 10 to the power 60 of those Planck times.  So that is what it means to say the universe is rather old.

It is amusing to try to visualise this number.  It is vastly smaller than anything in our experience.  I always like to do this little what I call ‘origami’ of the universe, with a sheet of A4 paper, (You probably know, we have A4 paper because the ratio of one side to the other side is the square root of 2, and if you add another A4, you will get A3, and the ratio of the sides is still the root 2.)  So suppose you wanted to fold this paper in half, how many times could you do it?  Well, I will give you £20 if you can do it more than 7 times.  You will not be able to do it.  But suppose you could.  Let us, instead of folding it, cut it with a laser cutter and keep cutting it in half.  Halving moves pretty quickly, because we would only have to half this piece of paper 30 times, and we would be down to the size of a single atom.  If you kept going, kept cutting it in half more and more, 47 times, you would be down to the size of the nucleus of an atom, 10 to the minus 13 of a centimetre, a single proton.  Keep going further, keep cutting in half, you would have to go 114 times and you would be down to about Planck length, the size of the visible universe at the beginning of that quantum era.  It is a lot of halving, but it is not unimaginable.

Suppose you went the other way, and you doubled the piece of paper, so we went to A3, A2, A1, A0 and so on, you would only have to double it 90 times before it became bigger than the whole visible universe today – 14 billion light years.  So just 90 plus 114, that is 204 doublings and halvings of this piece of paper, takes you from the smallest scale of physical reality up to the largest scale of physical reality.

Well, what happens after this Planck era, the universe begins to expand, it cools off a bit but, very quickly, we believe that something very dramatic happens.  After the temperature has just fallen by a factor of about 100,000, and the time has passed to around 10 to the minus 35 of a second, what happens is that some of the forms of matter in the universe have their temperature fall in a very sluggish way.  They do not cool off as fast as other forms of matter, like radiation, and they gradually have a bigger and bigger gravitational effect on the expansion.  Some of these pieces of matter exert a tension on one another, so they have like a negative pressure, and the effect of that, when it takes over the expansion, is to accelerate the expansion of the universe.  All of a sudden, it switches from slowing down rather gradually to a dramatic surge of expansion, and we call that surge inflation or the inflationary era, and it has a lot of consequences for the expansion of the universe.  In particular, it drives the expansion in such a way that it goes at the same rate in every direction, and it irons out huge disparities that could exist from one part of the universe to another.  It also drives the expansion towards a very critical rate, where its energy of expansion is almost exactly in balance with the energy of gravity trying to slow it down.  This difference sets up its expansion along a very particular course.

If we take a picture of this event from our perspective today, there would be us, sitting at the centre of this picture, and as we look out with perfect telescopes, we would be able to see about 14 billion light years.  That is the greatest distance from which light has had time to travel since the expansion began, and we call that the visible universe.  There is lots more universe beyond.  If we came back tomorrow, we would in principle be able to see a little bit further – one light day further.  But if we take the whole region, and run it backwards, run its history backwards, we can ask how small was the region from which it emerged or expanded from at any particular time.  And the effect of inflation, this dramatic acceleration in expansion early on, is to enable us to grow the whole of the visible universe from an extraordinarily small patch of space and time, so small that there is easily enough time for light to pass from one side to the other, to keep it very smooth and uniform and coordinated.  The remarkable uniformity in the universe today, the fact that it expands at the same rate in every direction, to one part in 100,000, and the graininess of the universe from place to place, is on the average also only about one part in 100,000.  This is the reflection that it inherits, the smoothness from one tiny microscopic patch of space.  If you did not have that surge of expansion, you would be growing the whole visible universe from a region that was vastly bigger, nearly a millimetre in size, and there would not be enough time for light to travel from one side to another, so one part of the universe would be very different from any other part, and that would be reflected in gross differences from place to place on the sky, in the temperature and the density of the universe today.

Another way of envisaging this in a more pictorial fashion is to imagine a little patch, in orange, which is going to inflate enough to have enough time and space for stars and galaxies and planets and us eventually to form.  If you could step beyond it, at that early moment, you would find other patches where things may be very different, and each of these patches will inflate by a different amount, some might not even inflate at all, and so you could imagine it like a foam of bubble being heated up.  We find ourselves necessarily in one of the bubbles that has expanded a lot, being enough time for stars to form and carbon to form and planets to form.  This is the short interlude that occurs when the universe is about 10 to the minus 35 of a second old.  It lasts only until it is about 10 to the minus 33 of a second old, so it is just like an instant but it has a dramatic effect on the future behaviour of the universe.  Towards the end of the lecture, we will look again and see that there is very particular observational evidence that we can inspect which seems to confirm that this sequence of events did indeed occur when the universe was very young.

Picture of the universe beginning and then expanding as we go forwards in time, and lots of things happen over that history.  So back at the apparent beginning, there is that quantum era, the Planck time as we called it.  You would see a great surge in expansion.  The universe becomes a lot bigger than it appeared destined to become because of the accelerating effect of unusual forms of matter.  And then it keeps on expanding, and keeps on cooling, as time passes.

The first dramatic thing that happens after inflation is what people call the Grand Unification Era or just the gut era.  It happens quite soon after inflation, and what this means is that we are reaching a watershed, and there are 2 or 3 of these watersheds in the evolution of the universe.  Physicists call them phase transitions.  The first one we met was back at the Planck scale.  You remember I said gravity started to go its own way, it did not remain bound in its strength and its behaviour to the other forces, and at the grand unification era, what happens is the strong pull, the force today which hold nuclei together, it starts to go its own way, and it leaves electricity, magnetism and the weak force of radioactivity bound together.

How can that happen?  Forces bind together when there are heavy particles which talk, as it were, to each of the forces, which act as carriers or intermediaries.  So if you have a particle that feels strong forces and feels weak forces, and it exists in profusion, then it can bind together the effects of the strong and weak forces.  But as the temperature falls, you may find the temperature is too low to produce those particles that you need any more, and that is what happens at this threshold.  The carrier particles suddenly cannot be produced by the heat radiation around in any profusion.  They decay and die out, and you do not have an intermediary to keep the strong and electro-weak forces bound together, so they go their own way.  But these decays, or these ex-particles, and their anti-particles, do something very dramatic.  Before this time, the universe does not have any imbalance between matter and anti-matter, it is perfectly symmetric, because it is so hot that these carrier particles are made in huge abundances, and if you try to have a little excess of matter, or anti-matter, you just throw up more carrier particles of the opposite sort that equalise the situation.  But as the carrier particles start to decay away, they do so in an unusual way.

Their decay products turn out to contain more particles than anti-particles.  Those particles are primarily what we call quarks – there are three of them inside every proton and every neutron.  So the result of these decays is to create a new sort of state in the universe, of super-quarks and anti-quarks, but where there is a little imbalance between matter and anti-matter.  Of course, it is purely nomenclature what you want to call matter and anti-matter – you decide that later – but there is an imbalance between the two sorts of material, and so it is at this time that we create an imbalance which later on will be responsible for our existence, and the existence of all the matter in the universe because, later on, the anti-particles will annihilate the particles and produce radiation.  This guarantees that there are some particles left over and those particles, eventually, become us, and there is about one of them, on the average, left over for every billion photons of radiation produced by the annihilation.  So matter in the universe is a one in a billion trace effect compared with the radiation.  This is an important chapter in the history of the universe.  It allows us to understand why there is a lopsidedness in the universe between matter and anti-matter, and the reason is that deep in the world of particle physics, there is not a symmetry between matter and anti-matter.  It is just an almost-symmetry.  You are always led to think that matter and anti-matter were the same in every respect, but they are not, and the particles decay at a different rate for the anti-particles and you get this imbalance.

Well, what happens after that, for a long time, is really rather boring.  There is a long period in the history of the universe that people sometimes call ‘the desert’ when very little dramatic happens.  It goes on until the temperature has fallen to about 10 to the 13 degrees.  It was 10 to the 27 degrees when that matter/anti-matter imbalance was created.

This cooling continues until you reach a time about 100 billionth of a second after the apparent beginning.  The expansion has grown by quite a large amount, by nearly a factor of 10 to the 20, so there has been quite a lot of expansion, quite a lot of cooling.  The universe contains lots of elementary particles, like neutrinos, quarks, anti-quarks, radiation, a few other heavy particles.  When it reaches this time and temperature, which in energy units are TeV energies, they are interesting because that is the sort of energy that we can attain in terrestrial accelerators like CERN today.  We are entering a regime where the conditions in the universe are like those we can simulate in colliding events and beams of particles in terrestrial accelerators, so we can start to bring together laboratory physics and cosmological physics to test ideas.

When we reach this time, we have another splitting of forces.  There is another watershed, and the watershed is between the force of radioactivity, the weak force, and those of electromagnetism.  With the strong force, we have some other particles, the W and Z particles as they are called.  There are three of them, so the W and its anti-particle, as an opposite charge, and the Z, which has no charge.  So these three particles have masses very close to this energy, and so when you are above it, you can keep making these particles from the radiation and their collisions with other particles, and they maintain this democracy between weak interactions and electromagnetic interactions.  W particles have electric charge and they carry weak charge as well, so they can carry out a dialogue, as it were, between things that interact only weakly otherwise and things only electromagnetically otherwise.

These particles, incidentally, the W and the Z, were predicted to exist back in 1967 when Steven Weinberg, with Abdus Salem and Sheldon Glashow, first developed this type of unified theory for this force, and at the end of the 1980s, as soon as accelerators could be built which could reach these energies, they were discovered at CERN in Geneva, with pretty much exactly the masses that were predicted, about 9 tenths of this energy, 90 GV.  So the W and the Z bosons were found in collisions at CERN.  Weinberg, Salem and Glashow were awarded the Nobel Prize for that discovery a few years later.

When the temperature falls below this, electromagnetism and the weak force start to go their own separate ways, and we start to see a world that is a bit more like the one we are familiar with in laboratory physics.

The next one of these watersheds comes up pretty quickly.  The temperature only drops by a factor of a thousand, the universe is only about one ten-thousandth of a second old, where something rather crucial appears.  The universe previously has been a soup of quarks and radiation, other elementary particles.  These quarks cease to just behave like a soup; they start to group up in 3s, and the triplets turn into protons and neutrons, particles of which you and I are made.  Some of the quarks pair with their anti-quarks to make particles like pion and other mesons, as they are known as in particle physics.  At this stage, there are no longer any free quarks in the universe.  Quarks have a strange property, that when you reach this lower temperature, they cannot remain free.  They have to be enclosed and bound inside particles like protons and neutrons.  This seems very odd.  If you had a proton, you would think, well, if it is made of 3 quarks, why can’t I just cut it in half, and one bit will have one quark in and maybe the other will have 2, and we’ll just see what the bits are.  Unfortunately, you cannot do that.  It is a bit like having a bar magnet and trying to convince someone that there is a north pole on one end and a south pole on the other and you really can just have a single magnetic pole, and someone says, ‘I don’t believe it – they always come in pairs.’  You will say, ‘Well, look, I just cut the magnet in half,’ so you make two magnets.  Where you cut, you produce another south and north pole, and you have got two magnets, with four poles, instead of a single loose magnetic quark.  This is what happens with quarks.  Quarks are joined together by little strings of particles called gluons, and if you try to cut the string, you release enough energy in the cutting to make another pair of quarks, and just as with the magnet, you end up with two pairs of quarks joined by strings.  So quarks swarm together rather like a collection of balls instead a rubbery bag, so every time they hit the walls, they bounce back inside; when they are in the middle, not near the walls, they hardly feel any forces at all; but as soon as they try to leave the bag, they hit the wall and they get banged back in.

This is a crucial event in the history of the universe.  This is when the little asymmetry and the number of quarks and anti-quarks suddenly makes itself felt, because when the quarks and anti-quarks find their way into protons and neutrons, we end up with slightly more protons and neutrons than anti-protons and anti-neutrons.  When the anti-particles start to annihilate the protons and neutrons, there is a tiny trace of protons and neutrons left over, so from this moment on, we have a universe that is essentially all matter.  Any other anti-particles that are formed are just made in collisions, as in cosmic rays hitting our atmosphere, so we say they are secondary.

These protons and neutrons then start to play an important role in the history of the universe.  We are at the most important time really in the early history of the universe.  It is an interval between when the universe is about a second old and about a thousand seconds old.  The temperature at one second is about 10 billion degrees; by 100 seconds, it is down to a billion degrees.  This sounds a very early time and a very high temperature.  Actually, conditions in the universe at this time are really quite moderate.  The average density of matter is just the density of water, so just like the density of these things around us.  We are not dealing with an environment with bizarre, unknowable densities and temperatures.  We understand very well the behaviour of matter and radiation at these sorts of temperatures.

What happens to the neutrons and protons is very interesting.  Weak interactions exchange neutrons for protons, so they keep undergoing reactions that turn one into the other, and then it goes back in the other direction at the same rate.  So while the rate is the same, the number of neutrons and the number of protons will be equal, everywhere, on the average.  Temperature starts to fall, you start to feel the effects of one of the strange coincidences of nature, and that coincidence is that the mass of the neutron is very, very slightly greater than the mass of a proton, and so to make a neutron requires a little bit more energy than it requires to make a proton, and so when the temperature starts to fall around the energy of the difference in mass energy of the neutron and the proton, an imbalance is set up.  You need more energy to make a neutron than a proton, so you tend to make fewer neutrons than protons.  The ratio of the number of neutrons to protons starts to fall below one, and if the reactions always continued, there would not be any neutrons in the universe – they would all just decay away and would not be replenished – but those reactions that keep them talking to one another and exchanging suddenly find the universe is expanding too fast for the reactions to keep up, and they turn off.  So the universe’s expansion is a way of turning off particular types of reactions, and these exchanges between neutrons and protons turn off, leaving a very particular ratio of neutrons to protons, one to 7.  So we started off with them being equal in number; we end up, at a time of about one second, with a one to 7 ratio. 

What is interesting about this is that long ago, in the 1940s, people started thinking about whether we could explain the origin of the elements – the elements that built up nuclei like hydrogen and helium and all the way to iron in the universe – and all those elements are made of neutrons and protons.  Originally, people thought that we might be able to use cosmology to predict the abundances of those elements, but one objection was, well, you could never do that, because the final abundances depend on how many neutrons and protons there were at the beginning of the universe, how many did you start off with, and nobody can know that, so we could never know the answer.

What this shows you is that the abundance of neutrons and protons does not depend on the beginning of the universe, all those things back at the Planck era and early times, because when the temperature is very high, the number of neutrons and protons are equal.  There is a thermal equilibrium between the two.  As the temperature falls, you reach this critical temperature where the equilibrium is broken and this very particular ratio is frozen in.  It does not depend on anything at the beginning of the universe.  This is the remarkable thing about the study of the early universe: at any one moment, the conditions that exist do not depend on how the universe began, because everything is internal equilibrium at earlier times. 

So we are in a situation with a very definite number of neutrons and protons, the temperature is nearly a billion degrees, and that means there are nuclear reactions.  Everywhere in the universe, a whole sequence of very, very fast nuclear reactions will occur.  By the standards of the previous exchanges between the protons and neutrons, these interactions are instantaneous – they are very fast, that is why they are called strong interaction.  Protons combine with neutrons to make deuteron, that is a type of hydrogen, so in the nucleus there is one proton and one neutron.  There is a very tiny part of this in sea water today, so deuterated water, D2O, as opposed to H2O.  To balance the momentum, you have a photon of light, and then 2 deuterons can combine to make Helium 3 and one neutron, so Helium 3, 2 proton in a nucleus, and one neutron, and you can go on and make tritium, another isotope of hydrogen one, proton 2 neutrons in the nucleus.  Tritium plus deuteron can make Helium 4 – that is 2 neutrons, 2 protons in the nucleus – and deuteron plus deuteron can make Helium 4.  And then there is a more ambitious reaction: Helium 4 plus tritium can make Lithium 7, so lithium is the next heaviest.

There is a whole chain of these nuclear reactions that occur very quickly when the universe is about three minutes old.  You can work it out: we know all the reaction rates, we know everything about these reactions we want to know, so we can start to create a little movie, as it were, of what goes on in the universe at this time.

Imagine a picture of passing time, with the temperature is in seconds, then we are at 100 seconds, If you remember at the beginning, neutrons divided by protons, one to 7, so there is one neutron for every 7 protons.  When the nuclear reactions begin, you begin to see the build up of various elements.  In particular, deuteron, H2, builds up, reaches a peak, there is a bit of destruction, and then it evens out.  Helium 4 fairly steadily builds up and then levels off.  Lithium 7, the lowest, reaches a peak, falls, and evens out.  The nuclear reactions start to build things up.  Eventually, the curves flatten out.  Because the universe is expanding and cooling, it shuts off the nuclear reactions fairly quickly, so the density of material to target becomes too low for the nuclear reactions to continue.  The universe is like a reactor that is self-regulating, and the final abundances will be those that we might expect to see in the universe today.  Some of the quantities, like lithium and deuteron, go up and then they come down again, and then they find themselves in the reactions in which they get destroyed, and they start to fall and then the reactions turn off and it levels out.  The remarkable thing about this is that you can predict, either by computer or you can do it with pencil and paper as well, pretty accurately, what should be the outcome of this sequence of primordial nuclear reactions in the universe. 

The final abundance is a fraction of the mass of the universe that ends up in the different forms, and is the measure of the density of the universe today.  I will describe why that plays a role in a moment.

The density of ordinary material made out of protons and neutrons, like you and me, in the universe, is the density of stars and rocks and planets and so forth.  The output has a slight dependence on that density, because back when the reactions take place, that density determines the density of targets for the nuclear reactions, and so obviously it is going to affect the rate at which they go.  Deuteron tends to be mainly destroyed after it is made so, as you increase the density, you have more destruction and you have less deuteron. All those deuteron nuclei that get destroyed get turned into helium.  Lithium gets destroyed and it gets made by a complicated battle between two interactions.

The prediction is about 22% of the universe’s mass should be in the form of Helium 4.  Almost everything else is hydrogen.  But there are tiny trace elements – this is 2 parts in 100,000, 2 times 10 minus 5 in the form of deuteron and Helium 3, and one part in 10 billion in the form of lithium.  Remarkably, these are essentially exactly the abundances that we see in the universe everywhere we look today.  We can’t make those elements anywhere else.  They are not made in the stars.  They are only destroyed.  This gives us a remarkable handle on what is going on in the universe when it has this remarkably small age.  There is a particular range of densities of matter in the universe which produce this nice concordant agreement. 

The interesting thing about that density is the so-called critical density of the universe that would be enough to make it eventually stop expanding and contract to a big crunch.  These observations enable you to deduce that the universe contained a hundred times really the material in the form of protons and neutrons and atoms of any sort to close the universe up.  It was one of the reasons that people started to suspect there were large amounts of dark matter in the universe, because today the dynamics of many galaxies and groups and clusters of galaxies behave as though they are responding to gravitational forces being created by about 50 to 100 times more material than is shown in my picture.  The implication is that it is dark material, and it is material that does not take part in nuclear reactions, and so plays no role in this story. There are beautiful candidates for that of course, particles like neutrinos, particles that just take part in weak interactions.  They do not play a role in destroying deuteron and building up helium.  From this picture and our observations of the dynamics of galaxies, we can not only infer that there should exist dark matter, we can say something about its identity, and in fact, if it is a neutrino, we can predict very precisely what its mass should be found to be in the next round of high energy physics experiments.  What we see between one and a thousand seconds, is that cosmology becomes a highly observational subject, so we can go out and look for these abundances of light elements.

After nuclear synthesis ends, we enter another rather distinct period of the history in the universe that I call the plasma era.  If we look back, we have begun at the Planck part, we have inflated, we have produced matter and anti-matter, we have separated the weak forces, we have had that area of nuclear synthesis, as it is called, where we made the lightest elements and, at the end of three minutes, that has come to an end.  We have now got a long period where the universe claims those very light nuclei, like helium and deuteron, lots of radiation, and lots of electrons.  The electrons are coupled to the photons to produce what physicists used to call a plasma.  Every electron scatters with photons and is coupled to the photons by these interactions.  There are no atoms in the universe at this period.  It is far too hot, with temperatures between a hundred million and 10,000 degrees, far too hot for there to be atoms.  Although there are nuclei, the electrons are not orbiting around them; the electrons are just scattering and are coupled to the particles of radiation.  This stage is what physicists call a plasma, and it is the sort of state that you would find at the heart of plasma reactors on Earth today.

One of the things that happens in this period of the universe’s history, like a great sea of radiation, is that the future course of structures and galaxies and clusters is dictated.  You see, if the universe tries to produce some clumps of material that are going to get bigger and bigger and turn into galaxies, it finds that it has a battle to fight with the radiation.  So if you have some electrons and nuclei, you want to make them a bit denser than the average so that they will attract more stuff.  The trouble is the radiation gets in the higher density region, and so it scatters more on the higher concentration and gradually pushes it apart.  If you try to have a bigger density of radiation, the higher temperature, the increased scattering, means the radiation just diffuses out into the background.  The effect of the radiation is to smooth out all small lumps and bumps that try to form, so if you want to start making a galaxy, or an embryonic galaxy cluster, in the early stage of the universe, it has to be so big that there is not time for the radiation to leak out of it or to pass from it to somewhere else.  During this period we get a special scale of size, so that below that size everything is smoothed out, and above it irregularities can survive, so from this period the characteristic scale of clusters of galaxies is imprinted on the universe.

As we get towards the end of this period, there is a sudden sequence of events.  Once the universe becomes about a quarter of a million years old, about 250-300,000 years old, the temperature falls and atoms can begin to exist for the first time.  So instead of the electrons being scattered by protons all the time, the photons have too low an energy to move the electrons away from the nuclei, and a proton will capture an electron, it will orbit it, and photons will not be able to remove it to ionise it.  For the first time, you enter an era when we have ordinary types of atom and eventually molecules.  This happens when the universe is a couple of hundred thousand years old, and the temperature starts to fall below about 1,000 degrees.  This is a crucial moment in the history of the universe.  Electrons combine and start to form the first atoms, and the photons of light are no longer being scattered everywhere by the electrons.  They are just flying freely between the atoms. 

If you tried to observe an earlier period of the universe, when it was much hotter than this, using a super-telescope, you would not be able to see anything.  It would be like looking at a piece of frosted glass, because to see, you require photons to fly freely to your telescope or to your eye, but in this earlier period of the universe’s history, photons are just scattering everywhere; they are not flying freely towards you.

Think what happens if you look toward the Sun, out of the corner of your eye.  What do you see when you see the Sun?  There is a disc, with an edge, and in the centre of the Sun, photons are behaving like they are in the early stages of the universe: they are scattering everywhere.  Eventually, they get to the edge of the Sun, where the density is low enough that they stop scattering and then they start flying towards you freely.  When you look at the Sun, what you see when you see the edge of the Sun is that last scattering surface, where the photons of light stopped scattering off other material and started to fly freely towards you.  So when we look into the early stage of the universe, with a radio telescope, if we wanted to see as far as we could possibly see, this is the moment that we could see.  Before that, the universe is opaque to light, but at this moment, it becomes transparent and the protons start to propagate through space and time towards us. 

After atoms start to form, eventually these great islands of material start to build up around those big, big lumps that survived the radiation plasma era, and those big lumps gather more material to them, they become more and more pronounced, they stop expanding with the universe and become what we call clusters of galaxies or just eventually galaxies forming within them, and within those galaxies, stars and planets will form.  This whole sequence of events that leads to structures is set in motion when the universe is a few hundred thousand years old, so first atoms, then galaxies, and then stars.

This last scattering surface of the universe is rather unusual.  If we had a radio telescope and we kept looking out at greater and greater distances from us, we should eventually be able to see that last scattering surface.  This is what satellite projects like WMAP and COBI have been doing in recent years – they have been observing that radiation freely flying towards us from the moment when the universe was about a quarter of a million years old. 

One of the maps that the WMAP satellite produced about a year or so ago is a temperature map.  If we imagine ourselves sitting at the centre of a sphere, as we look out from the centre, we will eventually see radiation all around us coming from that last scattering surface.  It showed a shell which gives the temperature variations on that last scattering surface, so the hot spots are red, hotter than average, and the purple spots are the cold spots, cooler than average.  Each colour change is a few hundred thousandths of a degree.  The temperature is really extraordinarily smooth, little variations.  If you are a statistician, you can do detailed analysis of this map and the data used to work out the detailed description of the statistics produced.

The beautiful thing about this, the reason people spend large amounts of money to make these sorts of pictures, is not just because they want to take a holiday snapshot of the last scattering surface of the universe, but you remember near the beginning of the lecture I mentioned how the inflationary universe, this surge of inflation, might have some observational signature?  When that little patch surges and accelerates and eventually becomes what we see today, there will be tiny quantum and statistical fluctuations in the patch that get stretched and amplified, and we can predict what pattern of temperature variations they should turn into on the sky.

The data points from two satellite missions of COBI and WMAP show that there really is a remarkable agreement, down to where the data is becoming pretty inaccurate because the scales are really tiny.  On small scales, things get damped out by the diffusion and smoothing I mentioned, but in the larger scales they survive.  It is rather like the ringing of a bell: you have a big peak, and then the oscillations just gradually die away.  Remarkably, we have a window into checking whether our description of the universe when it is 10 to the minus 35 of a second old is correct.  This is rather remarkable and, so far, the agreement between the simple theory and observation really is very impressive.  In the next two years, there will be another European mission which will produce more detailed observations, and will also look at something called polarisation of the radiation, so there is another property of the radiation you can predict in this theory, and we would like to check whether those predictions are correct as well.

During the era from when the atoms form and the radiation flies freely towards us to almost the present, something interesting goes on in the universe that we call gravitational ability.  This is something that Newton recognised should occur.  If you have a perfectly smooth distribution of material that is feeling the force of gravity, then if you just make it slightly irregular, you drop a few extra particles down within the smooth distribution, then it will get more and more lumpy and more and more irregular.  Why is that?  Well, if you add some extra particles then there is a bit more gravitational attraction, so those particles attract even more particles to them, at the expense of the others, so it is ‘unto those who have more is given, and those who have not, even what they have is taken away,’ as it were.  This gravitation instability is a snowball effect: denser regions become denser still at the expense of the sparser regions.  This is how, in the universe, a slightly irregular distribution of material and radiation becomes more and more irregular.  The lumps become more and more pronounced, so they are not just slight over-densities, but fully-fledged clusters and galaxies.  This process begins, and the amplification of irregularity commences, once the atoms form, when the universe is about quarter of a million years old.

Once upon a time, we thought that this process would go on essentially to the present, and you could still see lumps and bumps amplifying today, but in the last decade, with the help of the Space Telescope, we have discovered that the expansion of the universe has an extra ingredient to it.  We have discovered that, rather recently on the cosmic scale of things, about 4 billion years ago, the expansion began to accelerate, just like it did during that old era of inflation.  Most of the previous history of the universe it was decelerating, but it changes gear and has started to accelerate again.  It is rather mysterious.  We can pin down when this acceleration began: it began when the temperature had fallen to about 4 degrees, after about 9 billion years of expansion.  Today, the expansion is about 13.7 billion years old, and the temperature is 2.7 degrees.  So this moment is when the universe is about 75% of its present expanded extent.  If we go back, 25% smaller, a couple of degrees hotter, and then it starts to change gear and starts to accelerate.  This is very important, because once the universe starts to accelerate, you cannot make galaxies and clusters any more.  The universe expands so quickly when it accelerates that this gravitational instability is turned off.  Material gets whipped away from other material so quickly that having an extra density cannot compensate by dragging more material in.  Other material is being pulled away too fast.  So the whole process of making galaxies and clusters is turned off by this sudden change of gear.  That leaves us with something of a mystery: what is it that is producing this change of gear?

We conclude that it is a type of matter in the universe, of the sort that we understand because it was what created inflation at the beginning of the universe, so we know about this type of matter, and sometimes people call it quintessent because of that.  If we look at these observations more closely, then what we discover is it tells us what the energy budget must be in the universe today, or what is the stuff in the universe today, and 74% of it must be this quintessent material that has become known as dark matter.  It is a form of material that has a negative pressure that acts to accelerate the expansion of the universe.

There is then another 22% of material in the universe that is called dark matter, so this is the material that may be between the galaxies.  It is suspected to be neutrinos, the sort of material that dictates how galaxies rotate and how clusters move and their constituents move.  This is, possibly, a known form of elementary particle; it is something we might hope to detect in the future.

There is a tiny little trace element of 4%, which is all the atoms and ordinary things, of which you and I are made, and they are also the things that dictated how much deuteron and lithium and helium was made in the early universe.  These are the only things that take part in nuclear reactions.  These are probably weakly interacting particles, and we do not quite know what these might be at all.

What could that quintessence be?  The favourite candidate is that it is a sort of quantum vacuum energy, as it is called, for the universe.  If you have any system, any box, a universe containing matter and radiation that is governed by quantum theory, there is a lowest energy state that it can have.  If everything sort of comes to rest or you extract all the energy from it that you are allowed to extract, what is left will constitute what is called the vacuum energy, and that vacuum energy could be zero.  It was always suspected that it was going to be zero in our universe because it seemed to be very small, but it turns out that it is really not zero, and this quintessence is the evidence that it is not quite zero, but it is a complete mystery still as to why it is present in the amount that it is present; why it takes over the expansion of the universe after 9 billion years, not earlier, not later.  If it was a little bit earlier, we would not be here, because there would not be any stars and galaxies. 

The biggest mystery of all is those watersheds in the history of the universe that I stressed.  Remember the quantum gravity era; the one at the grand unification era, when the strong force goes its own way; the one at the electro weak era where the weak force goes its own way; and then when the quarks turn into protons and neutrons.  These 4 watersheds have a very unusual property: they inject into the universe a quintessence-like energy.  If you like, they dictate what the value of the quintessent energy should be.  So if you decide to start the universe off with a zero value, it does not help you for very long, because at the Planck time, when quantum gravity governs what goes on, it gets reinstated with a massive value of 10 to the 122.  You might decide, say, to start the universe with a sort of opposite value to that so that they just cancel out.  Well, it does not help you, because if you wait just a little bit longer, when the grand unification era comes along, it gets reinstated again, but this time with a value that is different, 10 to the 117.  Even if you found a way to stop that, at the electro weak transition, it gets reinstated again, this time with a value of 10 to the 108, and if you can get rid of that, then it gets reinstated again, with a value of 10 to the 105.  So this is very odd, because, well, what’s its value today?  In these units, its value is one.  So we have these processes going on in the universe that seem to want to make this quintessence energy vastly bigger than it could possibly be, so no one can understand what it is that stops these huge numbers when it goes through those transitions early on.  This remains the biggest unsolved problem of cosmology – why does the quintessence energy have the strange value that it does, and why does it start to accelerate the expansion?

We have talked about a universe that begins in an era of mysterious quantum-dominated expansion.  It expands and accelerates dramatically because of inflation, and we can check that by our observations today.  It then undergoes a long period of evolution, like a plasma, makes those lightest elements of helium and deuteron and lithium, and then eventually the radiation is freed and starts to propagate towards us, and we enter a long period of so-called cosmological dark ages, where the galaxies start to form, and only eventually do the stars start to shine, and then galaxies and clusters and planets start to form, until eventually, comparatively recently, this surge in the expansion begins, after 9 billion years, and all the galaxy formation is terminated.  Here we are today, looking backwards in time using satellites like WMAP to try to reconstruct our past history back in space, back in time.

© Professor John Barrow, Gresham College, 14 November 2006