The universe is expanding
Published on Feb 25, 2006 at 7:19 pm.
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Filed under cosmology.
A couple weeks ago, Tom posted an entry about galaxy NGC 1309. Here he mentioned the expansion of the universe, and sort of suggested that I say something about it. Now, I am doing just that.Â
So, to set the story, let’s go back to the early 20th Century. Alexander Friedmann, a Russian mathematician, was working with Einstein’s equations of general relativity. Now general relativity is often misunderstood. Yes, it is a description of the warping of space and time that leads to black holes, but it is more than that. Gravity is doing the distortion of spacetime, so general relativity is a theory of gravity. The distortion of spacetime due to mass is at the heart of the theory. Working with these equations, Friedmann devised an equation describing a metric, or a measure of spacetime in the universe. He found that his equation had two stable classes of solutions: either the metric is increasing or it is decreasing. The only way that it could be constant would be if there were no mass in the universe to distort spacetime. The implication of this is that the universe must either be expanding or contracting. This was a surprising finding. Einstein himself was so philosophically opposed to these results that he went back and arbitrarily added a term to the Friedmann equation that allowed for a class of stable solutions — neither expanding nor contracting. The strength of this term is given by a term called the cosmological constant.
In 1929, just a few years after Friedmann’s work was published, Edwin Hubble announced his findings that the more distant a galaxy were located from the Milky Way, the more quickly it was moving away from us. The relationship appeared linear. The recession velocity equals the distance times a number called the Hubble Constant. This could only be explained if the universe were expanding. The finding was so important that Einstein traveled all the way from Germany to California to meet with Hubble. After that meeting, he pronounced that his cosmological constant was the greatest blunder of his scientific career. So, the universe is expanding. Georges Lemaitre pointed out that the expansion of the universe, when run backwards far enough, resulted in all matter in the universe being squeezed into a very small volume. He proposed that running the universe backwards would even give the age of the universe. Such and age is given by the reciprocal of the Hubble Constant. His original idea was that all matter would be crammed into a single object, a sort of “primordial atom.â€Â This idea, though, was quickly abandoned and no cosmologist has believed that in almost 60 years, though some of the pre-college textbooks still teach the primordial atom. At any rate, Lemaitre’s model required that the universe have a beginning event. Being a priest, Lemaitre jumped on this idea as being consistent with his faith. Astrophysicist Fred Hoyle was unwilling to accept that the universe had a beginning, and he came up with his own model called the Steady State Model, in which the expansion of the universe opened up empty spaces in which new matter and galaxies came into being. Thus the universe would be infinite in extent and eternal in character. Hoyle was so opposed to the Lemaitre model that the even coined a derisive name for it: The Big Bang. He pointed out that it was ludicrous to expect that some sort of big bang could happen that would tear apart a primordial atom and hurl the bits out into space. Indeed physics does not support the concept of a primordial atom, and even Lemaitre agreed, adjusting his model not to require a single massive object at its beginning.
Along comes George Gamow and solved the problem of the initial condition of the universre. He showed that at high enough densities and temperatures, the particles that carry the forces of nature break down. At high enough energy density, for example, the electromagnetic force and the weak nuclear force become a single force called the electroweak force. Running the expansion of the universe backwards, you find that eventually all the forces merge into one force. Without the four forces, matter as we know it does not have the same properties. This permits the entire universe to be squeezed down to a single point, called a singularity. As the singularity expands, then the forces “freeze out,†particles begin to form, and then nuclei begin to form. Eventually, at the universe expands, it cools and atoms begin to form. The universe is like a giant cloud of gas at this point. This cloud then collapse into clumps that form the seeds for stars and galaxies. It is at this point that some of the details get fuzzy. It is important to note that a major difference exists here between Gamow’s model and Lemaitre’s model. Lemaitre at first proposed that material was hurled outward from a central object. Gamow proposes that space itself is expanding. Rather than things hurling outward, they are sitting still and space is expanding carrying objects farther from each other. This is really a significantly different model. This model is called the Big Bang model to distinguish it from Lemaitre’s primordial atom model which is called the Big Bang model. Hmm. Maybe that is why some of the pre-college textbook authors are confused. Actually, the modern view of this event is slightly different from Gamow’s model, and we call the modern model the Big Bang model. Yeah, right. A decade ago, Sky and Telescope had a contest in which votes were taken on what to name the newest version of the description of the beginning of the universe, and the winning name is ….. the Big Bang. Obviously, cosmologists don’t really have a flare for naming things. Try teaching this stuff. I get to say in class that “No one still believes in the big bang. Instead we believe that the proper description of the event is the big bang, which is a revision of the big bang, which replaced the earlier view of the big bang, which supplanted the big bang as the description of this event.
I don’t really have time to go into all of the observational evidence supporting this model. This blog is already going to be a long entry. Of course, I have my own observations of the expansion of the universe. I used to wear size 32 pants, but now wear size 34. That’s expansion of the universe, right, not just expansion of me? There are a couple of really good books, though, which explain the Big Bang very well. One, by Simon Singh, gives the history of the big bang models without any of the math common in detailed descriptions of the model.  It describes things in layman terms and is a very easy read.  Amir Aczel has written a very good book that gives a couple of the equations, but does not derive anything. It is written at about the level of Sky and Telescope, and it is very readable.  I have links to these books on my booklist.
Now for the strange parts of the modern big bang models. We know that the universe is expanding, but does it do so at a constant rate? The answer is NO. We know that gravity pulls on the universe, and that this should slow the expansion. For years, the holy grail of cosmologists has been to find the deceleration parameter, which would tell how quickly gravity is slowing the expansion of the universe. This is determined in large part by the density of matter in the universe. If the density is too low, then the universe will continue to expand forever, just going slower. If the density is too high, then the universe will collapse in on itself, in something called the big crunch. If the density is just right, exactly at some critical value, then it will expand forever, but will gradually come to a stop after an infinite length of time. There is only one critical value, but there are basically an infinite number of possible values of greater or lower densities. The chances of the universe randomly being at the critical density are basically zero. If we look out into space, we see only about 10% of the material needed to slow the expansion of the universe. However, when we look at the masses of galaxies or galaxy clusters we find that they have a mass about ten times larger than we get from looking at the material that we can see. We call this extra matter dark matter. Including dark matter in the equations gives a total mass and density VERY close to the critical value. So, how can the universe randomly wind up with a value that has almost no chance of happening randomly? For years, cosmologists have been trying to find extra mass which would result in the universe eventually collapsing in upon itself. Personally, I have never really understood this fixation with that particular solution. I have never had a problem with it expanding forever, but then I am not a cosmologist. I suspect that such solution, though, introduces some questions that many cosmologists are not comfortable with, so they try to avoid them. That isn’t really good science. Another problem facing cosmologists, though, was that the universe is too flat and homogeneous. In other words, you see the same thing, and make the same measurements, no matter what direction that you look. In particular, the universe is the same temperature in all directions. In order for two objects to be the same temperature, they must interact long enough to exchange thermal energy and reach equilibrium. The problem is that if you look in opposite directions in the universe, you see the same temperature. Yet, these parts of the universe are too far apart to have ever interacted. Thus, they can NOT be the same temperature. Yet they are. Hmm. A problem exists here.
Never fear, though, because my story isn’t over. Along comes Alan Guth. In 1979, Guth proposed that perhaps there might be a cosmological constant after all! In particular, he proposes that it isn’t really constant, but that it was large at one point, and then dropped to zero. When it was large, the universe expanded much faster than it does today. This period of rapid expansion is called “inflation.â€Â According to inflation theory, one of the forces didn’t freeze out quite as expected in the original Gamow model. The freezing out of the forces is much like a phase transition. It is known that you can actually cool water below its freezing point without it freezing if you do so carefully. This super cooled water will then freeze suddenly at the least little disturbance, with a sudden release in thermal energy.  Inflation theory proposes that something like that happened at one of the phase transitions in the early universe. The universe overshot for a fraction of a second the point at which the grand unified force came apart. When it finally did come apart, it did so with a sudden release of energy that the cosmological constant was briefly very large. Space itself suddenly expanded by a factor of perhaps 10 to the 50 power times. This would expand something the size of a hydrogen atom out to a distance of lightyears. In fact, it would carry much of the universe so far away that it would take longer than the age of the universe for light to reach us from that distance. So, all that we see would have essentially been at about one spot in the early universe, and so it would certainly have had time to reach thermal equilibrium. Inflation would stop at about the critical density of the universe. So, we now have an explanation for what we see.
However efforts continued to be made to determine the density of the universe and whether or not it will expand forever or collapse in on itself. Inflation might stop at about the critical density, but it would unlikely stop right at critical density. By the 1990s, technology had allowed measurements of the expansion of the universe to be made much farther than ever done before. This was, in fact, one of the goals of the Hubble telescope when it was placed in orbit — to measure the Hubble constant of the early universe. The slowing due to gravity actually means that the Hubble constant isn’t really constant. Over time, it will change. In 1998, I was at a meeting of the American Astronomical Society in which results from two teams of astronomers making just these sorts of measurements were reported. The fist of these speakers that I heard, Saul Perlmutter, gave surprising evidence that the universe, rather than slowing down, was accelerating its expansion! I had heard tidbits and hints of this finding, but I had not read any preprints, and had not heard details until then. Aczel’s book gives a better description. And Donald Goldsmith’s book is all about this accelerating universe. So, how does this acceleration of the universe’s expansion happen???
At present, we don’t really know why the universe is accelerating. Theorists are working overtime to explain it. The best explanation so far seems to be to look at the energy of space itself. We know that the universe is not empty.  Even in a vacuum, there are particles coming into being and then annihilating each other all the time. These are called virtual particles. They have an interesting effect. If you put two metal plates next to each other in a vacuum, there will be a repulsive force pushing them apart due to these virtual particles. These particles are responsible for the evaporation of black holes. Could they have something to do with the repulsion that is accelerating the universe? Another possibility, somewhat related, is that we have not only dark matter but dark energy in the universe. This dark energy could manifest itself in a repulsive force, like a non-zero cosmological constant, that would create an accelerating universe. Other more bizarre theories include energy leaking to or from higher dimensions of space, making it appear as if there were a repulsive force. Really, I don’t know if there is any agreement here as to why the universe is accelerating its expansion. Dark energy seems to be the best explanation. Again, though, I should point out that nothing is really moving in all of this. Rather space itself is expanding, and it is that expansion that is accelerating. The matter in the universe is just going along for the ride. Now if that isn’t enough to give you a headache — nothing is moving, but everything is getting farther away from everything else.Â
So, I am sorry that I can’t explain why the universe is accelerating, but it does seem to be doing so. If y’all want more, I can blog about this in more detail, but this seemed like a long post already.
Now, I’d be remiss if I didn’t point out that not everyone is on board with this accelerating universe thing. A few astronomers say that perhaps there is a problem with the distance measurements that Perlmutter made. He was measuring distances using Type Ia supernovae, which have a pretty uniform brightness. Material between here and these supernovae change their apparent brightness, which could throw off the measurements. Also, if stars in the early universe, which had slightly different compositions from stars today, exploded differently, then that, too, could throw off the results. The leaking energy people, who propose energy leaking to and from other dimensions of spacetime than the normal four that we see, say that perhaps this leaking energy can mimic acceleration. Other stranger ideas abound. However, various teams of astronomers have been reproducing the accelerating universe measurements using other means, so I think that we are safe to accept that interpretation of the measurements. Why? Dark energy seems the best guess so far.
-Astroprof
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