1 March 2011
The Book of Universes
Professor John D Barrow
Tonight, I am going to talk about some aspects of the development of cosmology. The study of cosmology and our understanding of the universe underwent a dramatic revolution in 1915. What happened than was that a picture and the modelling of the universe passed from being what was previously essentially a branch of Art History into Science. What I mean by that was, before 1915, in the centuries before, if you wanted a universe that was square or infinite or was balanced on the back of the tower of turtles, you could have it like that - you could imagine it to be like that. If you look across the history of many different cultures around the world, you find all sorts of different world pictures: some people thought the world was cyclic, some thought it was infinite, some thought it was finite. There was no way of generating precise pictures of the universe that were in accord with all the known laws of physics. But in 1915, Einstein created a new theory of gravitation, the so-called General Theory of Relativity, and the most remarkable thing about that theory was that the equations it supplied had solutions all of which were entire universes. So by solving these equations, if you were able to, you could produce possible universes which were consistent with all the known laws of physics. So, all of a sudden, you could produce candidates for possible universes which you could go out and test against the astronomical observations.
When Einstein did this, he discovered something that, at first, was rather surprising to him: he realised that his equations were predicting that the universe was not stationary or static, as everyone had always imagined; that space was not like a theatrical stage that was fixed and had planets, stars and comets moving around on it. The equations were telling him that their possible solutions tended to be where everything changed, either expanded or contracted into a gigantic lump of mass. He did not like this idea, and he noticed that, in his equations, there was the possibility for an extra piece of the gravitational force, a piece that was not just attractive, like Newton’s old gravitational force, but an extra part that was repulsive and got stronger as things got farther and farther apart, whereas Newton’s attraction got weaker and weaker as things got farther apart. Einstein liked this force because you could balance Newton’s attraction with his new repulsive force, and that would allow the universe to be static. This was the first solution, the first type of universe that was found from Einstein’s equations, which was found by Einstein himself. This repulsive force, which we will meet later on, is sometimes called the lambda force, or, the term that created it, the cosmological constant, Λ.
In this static universe of Einstein’s the distances do not increase at all, they are just always the same. The universe has no beginning, and it has no end. So the attractive force of Newton’s laws equalled Einstein’s repulsive force, and the universe had no acceleration:
Acceleration -GM/r2 +Λc2r
Unfortunately, rather quickly, this type of universe fell into disrepute. It is rather like having a needle which you balance on its point. Under perfectly stable conditions, it could remain balanced at that point, but the slightest disturbance, the slightest wiggle, will make it fall down. This universe has that sort of instability. With any slight movement in the universe away from perfect symmetry, it will either begin to expand or it will begin to contract. Therefore, this universe was not a viable, realistic possibility. Einstein very quickly came to appreciate this, and he called the introduction of this lambda force the biggest blunder of his life. Although, unfortunately, other people seized upon it, at the time, and found it rather interesting.
The next type of universe that was found from his equations was an expanding one, and it was found by a Dutch astronomer, Willem De Sitter. He decided to look for a type of universe where only the lambda force was present, or it was overwhelmingly bigger than Newton’s force, and this allowed a universe which expanded following an exponential trajectory. So, again, it has no beginning. You can follow it to a past eternity, it will get closer and closer to this zero, but never actually get there. And, likewise, it has no end in the future. We will see, later on, that this type of universe has turned out to be extremely important. It does not exactly describe our universe, but it plays an important role in our understanding of it.
Always expanding universe
Exponential curve R = exp[tLÖ/3]
No matter – only L
It has no beginning and no end (1917)
The person who first hit the jackpot and uncovered the key types of universe that are possible from Einstein’s Theory was a meteorologist and mathematician from St Petersburg, later Leningrad, and that was Alexander Friedmann. He was one of the first atmospheric scientists, and he did a lot of experimental work, but he was a formidable mathematician – a mathematical specialist in differential equations and curve geometries – and one of the few people in the world, like De Sitter and Eddington in this country, who had the mathematical knowledge that enabled him to understand Einstein’s Theory and to go about seeking solutions of these formidable mathematical equations.
Friedmann’s atmospheric science was somewhat reckless, in that, for a long while, he held the world altitude record for ballooning. So he would go up to enormous altitudes and do things that would surely be challenged by the Health & Safety Inspectorate today! He would calculate, for example, that when he reached a particular altitude, the air would be sufficiently thin that he would become unconscious, and then the trajectory of the balloon would be pre-calculated so that he would work out that he would regain consciousness at a particular altitude on the descent. In the meantime, his instruments would have been continually making measurements, during his period of unconsciousness. So he was a serious scientist, who died, as you can see, at a only 37, in 1925. He did not die in a ballooning accident, but undoubtedly from pneumonia and illnesses brought about by repeated extreme experiences at high altitude.
What Friedmann did was to solve Einstein’s equations with and without his mysterious lambda force, and he realised that there were just two types of universe: a universe that has some apparent beginning and keeps on expanding and carries on forever; and a more claustrophobic sort of universe that expands to a maximum and then contracts back to a big crunch. In between, there is a sort of British Compromise universe, that just manages to expand fast enough to continue forever.
It cannot be the same process that produced inflation near its beginning, but it is more like Lemaître’s universe. You will recall that it decelerates, changes gear, accelerates. Our point on the graph is marked, where this lambda force has apparently taken over and started things accelerating again.
What is mysterious about this, the reason it could be discovered, and was discovered, only thirteen years ago, was that you needed things like the Hubble Space Telescope, to be able to extend that Hubble-Humason law to see what happened to things that are very far away. When Hubble was used to do that, it discovered that that Hubble’s law was starting to slope upwards, that the velocity of recession of the most distant things was increasing with distance. What you found, in effect, was this change of gear, this acceleration, is occurring when the universe is about three-quarters, 75% of its present extent, about 4.5 billion years ago. Coincidentally, this is not very different from when the Earth and Solar System formed, but there surely cannot be any connection. So this type of universe that we see today has this mysterious acceleration going on at the moment, it has Einstein’s infamous lambda force in it, or something that mimics it almost perfectly. So the thing that Einstein thought was his biggest blunder has turned out to be one of his biggest posthumous successes, and Lemaître’s universe describes this trajectory extraordinarily well.
However, although one can produce a beautifully accurate description of the visible universe, using that Lemaître universe model, it is really very mysterious, and the big puzzle that people have had for the last thirteen years is: why has this acceleration suddenly happened so recently? So why does this lambda quantity have the particular value that it does? If it had had a slightly bigger value, just very slightly bigger, so 10 to the -120, instead of 10 to the -121, the acceleration would have begun just a little bit earlier, too early for any stars and galaxies to form, and we would not be here. So it is absolutely crucial to understand why this begins when it does.
Until quite recently, there had never been any suggestion, no way of explaining this, but in the last half-year, Douglas Shaw and I have developed a new sort of quantum cosmology which describes what happens in universes that have a lambda term in them. Although it is another lecture, suffice it to say that this theory is able to predict, fairly precisely, why Lambda has the value that it does, and therefore why it takes over today. But more importantly, it makes another prediction, a very precise numerical prediction, that can be tested, probably in about a year’s time – data has been taken, but it takes a year to reduce it by the Planck Satellite - that a fraction, 0.0055, of the energy in the universe is wrapped up in distorting the curvature of space, and that is something you can test directly with satellite observations.
The acceleration of the universe, this lambda term that makes it run away, is sometimes called dark energy, reflecting the fact that we do not really know what it is, but we know how to describe it, and its effect is gravitationally repulsive. About 73% of the universe’s energy is made up of this lambda force and its effects. Of the rest, 4% is composed of the stuff that you and I are composed of – atoms, molecules, and what physicists see as the uninteresting stuff – and 23% is in the form of what is called dark matter. We know dark matter is there because we can see its effects. It determines how the luminous material moves around, but it is almost certainly elementary particles of a neutrino-like variety, so they interact very weakly. At the moment, there are about 400 in every cubic centimetre of space, and they are moving around at about 250km per second, so millions are going through your head at this moment and you do not feel any ill effects. So they interact just weakly, not by electromagnetic interaction, not by strong interactions, and one of the main goals of the Large Hadron Collider at CERN is to find those particles. We can calculate what their masses should be and they are heavy enough that we could not have made them before in particle physics experiments – we need the much higher energies of the Large Hadron Collider. Rather neatly, the masses where we are expecting that they will be would also guarantee that they would be the first super-symmetric particles to be discovered, but that is another goal of the LHC. So, in the next couple of years, astronomers and cosmologists are hoping that this little mystery is going to be solved by the Large Hadron Collider, that we will find the new heavy neutrino particle that we have predicted, with a mass in the range that we have predicted, to fill in this bit of the story.
© John Barrow, Gresham College