Closing Thoughts:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
the universe at present contains considerable structure, in the form of galaxies, clusters, and superclusters. The distribution of dark matter, however, may be more uniform, and it is not yet clear just how non-uniform the gratitating material is on the largest scales
certainly, though, there is at least some structure, and this must have arisen from small uniformities in the early rather smooth distribution of material in the universe. Gravity would have led to small 'ripples' (regions of slightly enhanced density) growing with time, leading eventually to the formation of stars and galaxies. Indeed, computer models and simulations bear out this expectation (provided we are sure to include the ubiquitous 'dark matter')
the cosmic microwave background radiation has now been observed with sufficient sensitivity and resolution that we can confirm that the necessary 'ripples' were indeed present in the universe at the earliest stages. (If no 'ripples' had been found, we would be hard-pressed to explain how the galaxies and clusters of galaxies had come into being.)
for a time, it was puzzling to know why the differences in the CMB radiation received from different directions were so small. The implication is that the (possibly infinite) universe was at almost identically the same temperature everywhere in the earliest moments, since there would have been insufficient time for regions of different temperture to redistribute their heat and come to equilibrium. The uniformity of temperature seemed to be a special condition of the creation itself
this special feature was relaxed when Alan Guth introduced the notion of cosmic inflation, which explains that, in the first instants of the universe, a microscopically small region of the universe expands at a fantastic rate into a huge volume. Within this huge volume, the temperature would be everywhere the same, because of its origin in a yet smaller volume within which there had been time for equilibrium to be established. At this stage, what is now our entire visible universe would have occupied a still-microscopic part. After the inflationary phase, the more sedate Hubble expansion would continue as we see it now
the future of the universe depends on the forces which control the rate of expansion. Gravity can only work to slow the expansion, and the standard question for many decades was to work out the rate of this slowing. Would it, for example, lead to a reversal of the expansion, leading to the 'Big Crunch,' or would the universe instead expand forever?
one approach to this question is to look at remote galaxies, to see how much faster the expansion was in the early days. The problem is that galaxies evolve over time, and it is difficult to determine their distances
a better approach is to use supernovae, which can be as bright as whole galaxies and thus detectable at large distances. Since the fundamental nature of stars will not have changed for billions of years (although individual stars come and go), we can intercompare remote supernovae to nearer examples to work out their distances, and thus the distances of the parent galaxies (the redshifts of which are known)
these studies reveal that the universal expansion is not slowing down, but rather accelerating owing to an effect now dubbed the 'dark energy'. It is the dominant physical effect on large scales in the universe -- even trumping gravity -- but it is little understood so far. The universal expansion implies that we live in an infinite universe which will continue to expand at an acclerating rate until everything is infinitely scattered in the void
a single infinite universe has some disturbing implications, such as the inevitability of replicated versions of everything (if the Cosmological Principle truly holds)
there have also been serious scientific speculations about the possibility of there being an infinity of alternate universes, now and forever decoupled from our own, in many of which the very laws of physics may be different. This would give rise to universes of unimaginably different form, history, and potential
Associated Readings from the Text.Please look at: Chapter 22, pages 689-696.Motivation.The picture I have painted in the foregoing sections of the notes describes observational cosmology as it was up until a couple of decades ago. Attempts to understand the large-scale structure, present condition, and evolutionary state of the universe were predicated on the study of single galaxies as tracers of the motions. The trouble is that the samples were often small, and subject to the uncertainties imposed by our lack of a complete understanding of the evolution of galaxies. (I remind you that when we study remote galaxies, we see them as they were long ago, when still young. We need to understand evolution if we are to unscramble and comprehend the purely geometrical effects.) More importantly, we could not study the structure of the cosmic microwave background in adequate detail; yet it is the fertile ground out of which all other structure has subsequently arisen. Let us, therefore, consider what has come from the rich harvest of observations over the last fifteen years or so -- a time in history which has seen our astronomical understanding change in ways which have been very profound indeed. We start with the simplest of all questions: that of the growth of structure.The Present Structure.As I noted earlier, the distribution of material in the universe is not smooth. We see galaxies and clusters here and there, with apparent voids in between. Understandably, this was once interpreted as indicating that there was a large contrast between the dense 'starry' regions and the presumed empty space by which they find themselves surrounded. We now realise that this may be quite misleading! Don't forget that there is a considerable amount of dark matter in the universe. It may be spread quite uniformly everywhere, with the galaxies being little more than conspicuous beacons of light that don't actually contribute much of real substance. Here is an analogy: imagine a range of mountains of varying heights. Those that are exceptionally tall might be cold enough on top to be snow-capped; the shorter ones will not have any snow on them. Suppose, however, that you were flying high overhead and could see only the bright regions of white snow. You would get the impression of isolated patches of snow located in a few rare locations, with nothing of consequence in between. The many mountains that are only just too small to bear snowcaps would not even be noticed, although they are almost as imposing as their taller neighbours. The same reasoning may apply to the galaxies. It is possible that the dark matter is fairly uniformly spread, more or less everywhere, but that galaxies form only where the dark matter is, by chance, fractionally denser than average. Any galaxies that do form may blaze forth brilliantly and catch our attention, giving us the impression of a conspicuously enhanced region surrounded by near-complete vacuum. That is why is it so important to understand the total amount of dark matter present, and to figure out how it is distributed. (The best way to do this at present is to measure its gravitational lensing effects.)The Growth of Structure.By contrast to the present rather lumpy universe, the early universe seems to have been quite uniform in its properties. We know this principally because of our observations of the cosmic microwave background radiation: no matter what direction we look, the spectrum of the light is very closely the same, indicating that the radiation is coming from material that was at essentially the same temperature everywhere. But it cannot have been completely uniform: there must have been small variations in density from place to place -- 'ripples', if you like --- to act as the 'seeds' out of which the later regions of higher density would grow. Not surprisingly, it is gravity that leads to this growth: as the universe expands over time, the local gravity of a slightly denser-than-average region slows the expansion just a bit in its vicinity, and material accumulates there. As time passes, the gravitational force of the growing amount of excess material increases, and the effect accelerates until the density contrast becomes quite high, leading to the formation of stars and galaxies. Computer simulations show the effect of this process, and can explain the large-scale structure we see (sheets and walls of galaxies, huge voids, and so on) pretty successfully. (Dark matter has to be included.) But this only works if there were indeed some small irregularities to begin with, and, if so, we should be able to see suggestions of that in the cosmic microwave background (CMBR). The density differences would show up as slight temperature differences, with some small regions appearing to be fractionally hotter than others (a few thousandths of a degree!). The earliest observations of the CMBR did not have the necessary sensitivity or angular resolution to map out these subtle differences, but more recent experiments have done so with amazing precision. (The first to do so, almost twenty years ago, was the COBE [COsmic Background Explorer] satellite, with findings which were vastly overblown by the public relations mill! The discoveries were described as equivalent to 'seeing the Face of God' and so forth.) I am not concerned that you understand the details, which are complex in their interpretations; but please look at the figure on page 716 of your textbook to see just how well we can explain the variations in temperature that we measure at various locations around the sky in terms of the theoretical models which describe how the structure starts its development from slight irregularites. The way in which these theoretical models are matched to the observations constrains all sorts of parameters, and provides excellent determinations of the age of the universe (a bit less than 14 billion years), the average density of the matter within it, and so on.Why So Uniform?So far, this may all sound like a litany of success, but in fact things are more complicated than that. I noted that the CMBR has very nearly the same spectrum no matter the direction in which we look, and that this implies that the universe was quite uniform at a very early stage. But this is actually a puzzle -- in some senses, it is 'too good to be true.' The problem facing astronomers twenty or more years ago was to understand how the CMBR radiation coming from these different directions could be so closely the same. One way to understand the problem is to imagine yourself in a bathtub which is just a bit too cool for comfort. You turn on the hot water tap at one end, but that will not immediately raise the temperature of the whole bath. You would have to wait for the bath to reach its new warmer equilibrium as the heat flows from the hotter regions to the cooler (or, more efficiently, to swirl the water around with your hands to hurry this process along). The early universe presents the same problem. The CBM radiation was emitted by the omnipresent material in the hot dense early phases of the universe. If we look in diametrically opposite directions, we are looking at regions of matter which were already fairly widely separated by the time they emitted the photons we are now collecting. It is certainly true that the different lumps of material whose radiation we are detecting from those separate directions were much closer together in the early times. But the universe was expanding rapidly at that time, and was too young for radiation to have made its way back and forth between these two lumps, despite their closer proximity then. There was, in other words, no time for them to 'communicate' with each other and to come into temperature equilibrium. The inescapable conclusion seemed to be that, for some reason, the universe came into existence with exactly the same temperature everywhere -- a 'special condition' that seems to be unmotivated. We would rather understand why there were not some random fluctutations of moderately large size.Inflation.A remarkable solution to this came from the imaginative mind of the young physicist Alan Guth. He was the first to suggest that the early universe underwent a period of what has become known as cosmic inflation. He also suggested a physical mechanism and justification, and although there were problems with his treatment, he is rightly to be acknowledged as the originator of this remarkable insight. (The failings in his discussion were subsequently addressed and resolved by others.) Cosmic inflation is a remarkable and anti-intuitive phenomenon, and I will not belabour it here. It is described on pages 712-717 of your text, where several of its successes are described. (Among other things, it resolves the so-called 'flatness' problem, which I have not described.) But let us take the time to understand how it solves the particular problem of the remarkable temperature uniformity of the CMBR. The answer is simplicity itself. According to inflation, an infinitesimal volume (a trillion-trillionth of a centimeter in diameter) expanded at a fanatastic rate, to a volume which was 100 million light years or so in diameter -- growing by fifty powers of ten in a less than a million-trillion-trillionth of a second! (The numbers don't matter. Let us focus merely on visualising the phenomenon.) But this happened so early in the cosmic history that even after the inflationary epoce the density was still enormous, with all the material now visible to us in the universe still contained within a volume less than a million-trillionth of a centimeter in diameter. Only then did the much more sedate Hubble expansion continue in the way that we now see it. You can see why this resolves the temperature problem. At a very early stage, all the material in the visible universe was much more closely packed than a simple 'backwards extrapolation' of the Hubble law would suggest, and there would have been no problem for the material to reach thermal equilibrium. The inflationary period then spread this nearly-uniform material over a much larger volume, and the successive period of Hubble expansion leaves us in a universe where the radiation from all regions has very much the same spectrum, as we see it. On the very largest scales, many orders of magnitude larger than our entire observable universe, there could well be significant temperature variations -- but we started inside a pre-inflationary volume which was in complete equilibrium and remained so until the time of the emission of the photons which now constitute the CMBR. As implausible as inflation may sound to you, there are in fact well-understood fundamental physical principles that underlie and motivate it. Moreover, as noted above, it resolves several other problems, not just the temperature uniformity.Back to the Future.In a previous section of the notes, I explained the importance of determining the geometry of the universe: that will decide its eventual fate. As I noted, the 'classical' approach was to study the galaxies themselves, to try and determine whether or not the remote galaxies were receding faster in the early days and have subsequently slowed down significantly. If so, the implication would be that the universe has sufficient gravitating material within it -- including gas, stars, and dark matter -- to eventually reverse the expansion. The problem, described earlier, was that the galaxies themselves evolve significantly with time. Unfortunately, the distances of the really remote galaxies can only be determined by assuming that they are comparable to their nearer counterparts, an assumption that is probably increasingly incorrect the farther out we look. Unless we know the 'evolutionary corrections', we cannot work out the geometry (and vice versa). Fortunuately, there is a better way: use supernovae as distance indicators.Supernovae.As you may remember, supernovae can be as bright as entire galaxies; moreover, the light of a supernova is concentrated in a bright, conspicuous point of light, easily measured and quantified. But the greatest advantage to using supernovae is that stars are stars, by which I mean that a supernova which happened ten billion years ago is expected to be essentially indistinguishable from one happening today. So we can safely assume that the faintness of a remote supernova is entirely attributable to its distance: we don't have to worry that supernovae 'in the old days' were much brighter, or much fainter, than their present counterparts. This allows us to determine distances to the galaxies which are the homes of the supernovae, and then to consider how the observed redshifts of the galaxies depend on their distances. Obviously, the observation of a single supernova in a remote galaxy would be a pretty weak indicator on which to base any conclusions about the fate of the universe! You would much rather have a lot of data, which is the reason that the automated searches for supernovae have been such important astronomical observing campaigns in the last decade or two. Programs of this sort have discovered many remote supernovae, ideal for the purposes of determining the history of the cosmic expansion and, by inference, its predicted future behaviour.The Surprising Result.Astonishingly, the supernova observations reveal that the universal expansion is actually accelerating. This would not and indeed could not happen in a universe dominated simply by gravity, so it appears that there is some new physics at play -- an effect that has the effect of a cosmic repulsion on the largest scales. This seems obviously akin to Einstein's cosmological constant, although in fact it enters in a slightly different way than Einstein had introduced his 'lambda term.' Still, it is remarkably like his early inclusion of a repulsive effect, and it may be that he was essentially right in yet one more way. As noted, though, its modern description is in terms of a 'dark energy' that will increasingly dominate the evolution of the universe: this is not quite what Einstein had in mind, although the distinction is rather subtle. The growing importance of the dark energy depends on the scale over which it operates. It is possible, for example, that it will serve merely to scatter the galaxies increasing quickly to effectively infinite distances, leaving the Milky Way (many billions of years hence!) in supreme isolation. On the other hand, it is possible that the dark energy will become increasingly important on smaller and smaller scales, in which case even individual atoms will feel internal disruptive forces which tear them apart. We do not yet know!Absolutely Final Remarks.It would seem that the universe is infinite in extent, and will never recollapse. The accelerating expansion implies a future in which we find ourselves in an infinite void, which some people find disturbing. But there are other aspects of infinities that are worth thinking about. It is, for example, interesting to consider the implications of a truly infinite universe in which the laws of physics are the same everywhere and in which the average conditions on large scales are similar -- that is, a universe in which the Cosmological Principle is obeyed. If that is the case, then any particular arrangement of atoms in any particular volume will be replicated an infinite number of times. This seems to imply that there are an infinite number of galaxies identical to our own -- plus an infinite number that are very close to it, differing in only some insignificant way; plus an infinity of galaxies that are a little less like the Milky Way; and so on. (That is what infinity means!) Please note that I said 'identical', and I mean literally that: there must be an infinite number of arrangements of atoms that identically replicate what we see in the Milky Way, including the positions and orbits of the stars, the planets and asteroids surrounding those stars, the rocks and trees on those planets -- and you and me. When I consider the notion of an infinity of 'myselves' (plus an infinity of slightly less-close matches, and so on), I find the notion very troubling, especially insofar as to what it means about free will. Since there will be an infinity of situations that differ only microscopically from ours, there will be a host of different futures depending on how circumstances evolve from there. Disturbing! This notion leads rather naturally into a concept that has lately been developed in the elegant writings of Martin Rees (although the notion is not new). Martin speculates that there may in fact be an infinite number of universes, completely and forever disconnected from our own (and thus forever unknowable to us). In these universes, the laws of physics themselves may take different forms, so that some universes may be sterile and uninteresting, while others are vastly richer than our own, in ways that we cannot even begin to comprehend. It is possible, for example, that the formation of a black hole, with its singularity in space and time, marks the spawning of yet another universe. In these quick jottings, I cannot pretend to do justice to these thoughts, but would encourage you to read Martin's wonderful book "Before the Beginning" for an exposition that is both accessible and profound. In class, however, I closed with the playing of a particularly appropriate excerpt from a wonderful composition: the First Symphony (the "Sea" Symphony) of Ralph Vaughan Williams, in which he set to music some of the evocative words of the American poet Walt Whitman: O thou transcendent, Nameless, the fibre and the breath, Light of the light, shedding forth universes, thou centre of them. I could not imagine a more profound thought on which to end. Previous chapter:0: Physics 016: The Course Notes, spring 2005. 1: The Properties of the Sun: 2: What Is The Sun Doing? 3: An Introduction to Thermonuclear Fusion. 4: Probing the Deep Interior of the Sun. 5: The Sun in More Detail. 6: An Introduction to the Stars. 7: Stars and Their Distances: 8: The HR Diagram: 9: Questions Arising from the HR Diagram: 10: The Importance of Binary Stars: 11: Implications from Stellar Masses: 12: Late in the Life of the Sun: 13: The Importance of Star Clusters in Understanding Stellar Evolution: 14: The Chandrasekhar Limit: 15: Supernovae: The Deaths of Massive Stars, 16: Pulsars: 17: Novae: 18: An Introduction to Black Holes: 19: Gravity as Geometry: 20: Finishing Off Black Holes: 21: Star Formation: 22: Dust in the Interstellar Medium: 23: Gas in the ISM: 24: The Size and Shape of Our Galaxy: 25: The Discovery of External Galaxies: 26: Galaxies of All Kinds: 27: The Expanding Universe: 28: Quasars and Active Galaxies: 29: The Hot Big Bang: 30: The Geometry of the Universe: 31: Closing Thoughts: Part 1:Part 2:Part 3: |
(Wednesday, 22 April, 2026.)
