Chapter 5 Cosmology

  Cosmology began as a scientific discipline at the beginning of the 20th century, with the work of Albert Einstein and Edwin Hubble. It was Einstein that provided the theory within which it was possible to sensibly consider the entire Universe, and it was Hubble that provided some of the first observations that showed the Universe was expanding. Before the 20th century neither of these things had been possible, and cosmology had remained almost exclusively within the province of religion and philosophy. Since then it has flourished as a science, and it is currently in the process of becoming a precision science.

  The gravitational interaction is fundamental to the study of cosmology, as gravity dominates over all other forces on large distance scales. Unfortunately, it is not possible to create consistent models of the Universe with Newton’s theory of gravity alone. This is because Newton assumed that his inverse square law of gravity is applicable to everything in the Universe, and that it is transmitted instantaneously. This means that, according to Newton, the gravitational field we experience on Earth should be a sum of the gravitational fields of every object that exists in the entire Universe. This isn’t necessarily a problem by itself, but it does become problematic if you try to add up the gravitational fields of infinitely many objects. In this case it turns out that Newton’s theory tells us that the total gravitational field at any given point in the Universe depends on the order in which we add up the gravitational fields of all of these objects. This is obviously not a very satisfactory situation.

  Of course, we now know that Newton’s theory is only an approximation of the more complete theory developed by Einstein. Thankfully, the problem described above does not occur in Einstein’s theory. Instead, we get a rich set of models that are self-consistent, and that can be used to model the Universe we see around us. In fact, because of Einstein’s focus on space and time, we get a much deeper understanding of the Universe through his theory than we ever would have got from Newton’s. This is because, using Einstein’s theory, we are not only able to model how objects in the Universe move, with respect to each other, we are also able to create a model of how the space and time that make up the Universe behave. Let us now consider this in more detail.

  The modern history of cosmology

  Modern cosmology, as we now understand it, began in Russia in the early 1920s with the work of Alexander Friedmann. Using the recently published General Theory of Relativity, Friedmann showed that a universe that was the same at all points in space, and that looked the same in all directions, should be expected to either expand or contract. This remarkable prediction must have come as quite a surprise, because at this time no astronomer had been able to reach such a conclusion using observations. Nevertheless, Friedmann was able to produce a set of equations that such a universe would have to obey, and had even been aware that the geometry of space in these models could either be flat or have positive or negative curvature. That is, he was aware that there existed solutions to Einstein’s equations in which the geometry of space could be curved, like the surface of a giant three-dimensional sphere, or the surface of saddle (see images in Figure 10).

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  10. Examples of spaces with constant positive curvature (k 〉 0), vanishing curvature (k = 0), and negative curvature (k 〈 0), respectively.

  Friedmann was a pioneer, but his work was not widely recognized at first. He was initially criticized by Einstein, who thought he was in error. Einstein later introduced an alternative model of the Universe, which he forced to be static by introducing a new term into his equations that he called the cosmological constant. This model was shown to be unstable by the Belgian priest Abb』 Georges Lema’tre, who was developing similar ideas to Friedmann towards the end of the 1920s. In fact, Lema’tre, who had been a colleague of Sir Arthur Eddington, had written in a scientific paper in 1927 that observations suggested that the Universe was indeed expanding, in what later became known as Hubble’s law. The article containing this monumental discovery was initially published in French, in an obscure Belgian journal. Strangely, when it was translated into English, in 1931, the section on Hubble’s law was missing. Nevertheless, Lema’tre is remembered today as one of the most important figures in the development of modern cosmology.

  Friedmann and Lema’tre were both mathematicians, and although the latter had a good knowledge of astronomy, it was not until the astronomer Edwin Hubble published his famous results in 1929 that cosmology really got started as an observational science. Hubble showed the world that the Universe was expanding. He did this by calculating the distances to what we now refer to as galaxies, and by using known information about their motions. Hubble showed that the recessional velocity of a galaxy is proportional to its distance from us (so that, e.g., if galaxy A is twice as far away as galaxy B then it should recede at twice the velocity). This is just what Lema?tre had predicted from Einstein’s theory, and it proved beyond reasonable doubt that the Universe was indeed expanding. Einstein gave up on the idea of a static universe, and described the cosmological constant as the 『biggest blunder』 of his life.

  The expansion of the Universe might perhaps seem like quite a diferent phenomenon to those we usually think of as being due to gravity, but it isn’t really. The large-scale expansion of the Universe is intimately connected with gravity. In a very real sense, one can think of the expansion that Friedmann, Lema’tre, and Hubble discovered as being due to nearby galaxies falling away from each other under their mutual gravitational interaction. As a more domestic example of the same phenomenon, consider throwing a tennis ball directly upwards into the sky. Normally the tennis ball will reach a maximum distance from the surface of the Earth, before it starts falling back down. In the period before this, however, when the ball is travelling upwards, it is still being acted on by gravity, and it is by using the equations that govern the gravitational force that we can calculate the properties of its motion, such as how fast it will be moving at any given time in the future. Two nearby galaxies are very similar to this. The galaxies may be moving apart, but the rate at which they move, and whether or not they will fall back towards each other, is dictated by the gravitational force between them. Einstein’s theory simply allows us to construct a consistent picture of an entire Universe filled with objects that are 』ying away from each other.

  The tennis ball analogy raises an obvious question. If galaxies are 』ying away from each other, like the tennis ball 』ies upwards from the surface of the Earth when we throw it, then does this mean the galaxies will eventually stop 』ying apart, and start falling back towards each other？ Or in other words, could the Universe eventually stop expanding and start to re-collapse？ This is a perfectly good question, and the answer can again be given by considering the tennis ball. If instead of throwing the tennis ball upwards we launch it at high speed, from some super-powered cannon, then it’s possible it might never come back down to Earth. Scientists call the speed required to make this happen the escape velocity, and it’s very easy to calculate. If the tennis ball is launched at a speed greater than the escape velocity then it will never return to Earth. If it’s launched with a speed less than the escape velocity, it will eventually fall back down. The situation with galaxies is very similar. If they are receding away from each other with suicient velocity then they should be expected to 』y away from each other forever, and the Universe should then be expected to expand forever. If the rate of recession is too low, then the galaxies will eventually fall back towards each other, and the Universe will start to collapse. The rate of recession between galaxies is known as the Hubble rate, and the velocity required to make them 』y away from each other forever is known as the critical rate. Theory doesn’t tell us if our Universe is expanding above or below the critical rate. To discover this, we have to point our telescopes out into space, and observe.

  By observing the expansion of the Universe, we therefore have another way to observe the consequences of the gravitational interaction. Indeed, in this way we can ask and answer questions about gravity that cannot be easily probed by experiments in the Solar System. These include questions such as: Has gravity always had the same strength？ Does light have its own gravitational field, in the way that Einstein’s theory predicts？ And what happens to gravity when the density of matter becomes very large？ The reason why we can answer these questions in cosmology is because of the very large length scales involved; because of the fact that the Universe is expanding; and because of the finite speed of light. Let’s think about how this works.

  In most situations in life we’re used to the idea that we can see what’s happening, as it happens. However, this isn’t quite true. It just appears that way. Because light has a fixed velocity (about 300 million metres per second), it takes some time for the light emitted or re』ected of an object to actually reach our eyes. The speed of light is very high, so we don’t usually concern ourselves with this delay. When an object is very far away, however, the delay can become significant. If the Sun suddenly exploded, for example, it would take more than eight minutes for us to know anything about it, because that’s how long it takes the light emitted from the Sun to reach us (and nothing can move faster than light). Another way of thinking about this is that when we look at the Sun we see it as it was a little over eight minutes ago. The same thing happens in cosmology, but the observable Universe is very much larger than the distance from the Earth to the Sun, so the efect becomes huge. For example, it takes more than four years for light from the nearest stars to reach us, and some tens of thousands of years for light from the nearest galaxies. If we look even further away we see objects as they were billions of years ago. In a sense, we can see back in time by looking far away, and if we look far enough away we can see what the Universe looked like when it was very young.

  Now, it’s a well-known result in thermodynamics that when you compress an object (like a balloon full of air), it gets hotter. Likewise, if you make the same object expand then it gets cooler. The Universe is no exception to this rule. If we think of the expanding Universe as playing on a movie reel, then if we run the reel backwards we should expect to see the Universe getting smaller and hotter, until at very early times it bursts into 』ames. Now recall that we can in fact see the early stages of the Universe’s evolution, and you might expect that we should see a fireball if we look far enough away (and hence, look far enough back in time). This possibility was first predicted by Ralph Alpher and Robert Herman in the late 1940s, but it wasn’t until 1965 that it was accidentally observed by the radio astronomers Arno Penzias and Robert Wilson. The signal they detected is now known as the CMB, or the Cosmic Microwave Background.

  The discovery of the CMB confirmed to the world that astronomy could be used to see the very early stages of the Universe’s evolution, when it was in an entirely diferent state of being. At the same time it opened the door to testing gravity in wildly new environments, where the gravitational field of light could be stronger than that of normal matter, and where we can consider time and distance scales that range over the entire observable Universe.

  The early Universe

  Since the early days of the 1960s, cosmology has blossomed into a well-studied field of both observational and theoretical physics. The positions of hundreds of thousands of galaxies have been mapped, we』ve seen astrophysical events that occurred many billions of years ago, and the CMB that Penzias and Wilson discovered has been measured to incredible accuracy. These observations, and others, have been used to give precise answers to questions such as 』How old is the Universe？』, 』Will the Universe expand forever？』, and 』What types of matter exist in the Universe？』. The answers to these questions are somewhat puzzling, but have profound consequences for our understanding of gravity. We will consider them in this section.

  Let’s start at the beginning of time. If the Universe was smaller and hotter in the past, then if we consider earlier and earlier times, then the density of matter should be expected to become larger and larger. Now, it turns out that not all types of matter increase in density at the same rate, as we go back in time in this way. The density of light (or radiation, as it’s often referred to by physicists) increases at a faster rate than the density of most other types of matter. This means that at very early times the density of radiation can be even higher than the density of the electrons, neutrons, and protons that make up normal matter. In this case the gravitational field of radiation becomes the dominant in』uence on the expansion of the Universe.

  The radiation-dominated stage of the Universe’s evolution is relatively brief. It only lasts for the first few tens of thousands of years after the Big Bang. Nevertheless, it is an extremely interesting period of time, particularly for the study of gravity. One of the physical processes that takes place during the radiation-dominated period is the synthesis of the light elements (hydrogen, helium, lithium, etc.). Among the many factors that in』uence this process, one of the most important is the expansion rate of the Universe. Detailed calculations, and observations of the amounts of hydrogen and helium we see in the Universe around us, allow us to place tight constraints on the gravitational field produced by radiation in the very early Universe. The results of such studies are consistent with the predictions of Einstein’s theory, with uncertainties at the level of only a few per cent. This is less precise than observations of gravity in the Solar System or in binary pulsar systems, but it’s not bad considering it involves testing what happened billions of years ago.

  As well as the synthesis of light elements, however, there are other interesting physical processes that take place during the early stages of the Universe’s history. One of these is the process that eventually leads to the formation of the first astrophysical structures in the Universe. It’s been known since the findings of Penzias and Wilson that the early Universe looks very close to being perfectly smooth. Very close, that is, but not exactly so. There are small ripples in the CMB radiation that these astronomers found, and these ripples are thought to be the seeds of what eventually turned into the complex network of galaxies and clusters of galaxies that we see around us today. It is gravity that was responsible for the collapse of these small ripples into galaxies, but before this occurred gravity still played a crucial role.

  In the early Universe there was a battle between gravity, on the one hand, which tends to make matter clump together, and radiation, on the other, which interacts with the matter, and can cause it to spread out. Any small 』uctuations that exist in the interacting soup of matter and radiation therefore start to oscillate, as they’re pulled together by gravity, and pushed apart by the radiation. The period of these oscillations depend on their size in space, but are easy to calculate. This 』uctuation in the density of matter continues until the Universe cools to a suicient degree that it becomes transparent (at very early times it’s opaque, like a fireball, as discussed before). At this stage the radiation can stream past the matter, and reach the telescopes of distant observers billions of years later, with very little interruption. The CMB that Penzias and Wilson discovered is made up of exactly this type of radiation, measured more than thirteen billion years after the fireball ended. The efects of the war between gravity and radiation are imprinted as tiny ripples in the CMB. These ripples contain a lot of information about the rate of the Universe’s expansion; the amount of radiation in the Universe; and the ways in which radiation and other types of matter interact. They also contain information about the space through which the radiation has travelled, before we observe it on Earth. In short, the CMB is a scientific treasure chest.

  Detailed observations of the CMB first began with the launch of NASA’s Cosmic Background Explorer (COBE) in 1989. This satellite experiment observed the background radiation over the entire sky, and showed that the radiation was of exactly the form one would expect if it was emitted from the primordial fireball. The COBE experiment also made the first attempt at observing the small ripples we just discussed. In the end, COBE didn’t have the resolution required to extract much information from these ripples, but it made a promising start. Since then, a series of balloon-based experiments have been performed. Among these were the BOOMERanG and MAXIMA experiments, which were launched in the late 1990s. The detectors in these experiments had suicient resolution to see the largest of the ripples, and this was enough information to determine that the Universe was extremely close to the 』critical』 value of expansion, right at the borderline between re-collapse and eternal expansion. For this to be compatible with the rate of expansion we see around us in the Universe today, however, it looked like something strange had to have happened. Something had to have sped up the Universe’s expansion between the time of the fireball and now』and by some considerable degree.

  Background radiation experiments took another leap forward at the beginning of the 21st century. In 2001, NASA launched the Wilkinson Microwave Anisotropy Probe (WMAP) into space. The WMAP experiment was able to see not only the largest of the ripples, but some of the smaller ones too. This was tremendously important, as it allowed the processes involving the growth of these ripples in the early Universe to be made the subject of observational scrutiny. This was followed, in 2009, by the launch of the Planck Surveyor, by the European Space Agency. Planck was a step beyond WMAP, and allowed many more of the ripples to be measured. The results of WMAP and Planck were a glorious confirmation of the theoretical physics that had been developed to understand the growth of the ripples in the early Universe. They showed that the collapse due to gravity expected from Einstein’s theory took place just as expected, and that the amount of radiation in the early Universe was compatible with that required by the primordial nucleosynthesis calculations. They also found, however, that there appeared to be a large amount of matter in the Universe that didn’t interact with radiation in any way, other than through its gravitational field. This isn’t how normal matter behaves.

  The background radiation contains further information beyond what I』ve just described. Some of this I』ll describe later on, as it is more a prospect for the future rather than something that has already been detected. It’s worth mentioning here, however, that as the radiation travels through the Universe, from the primordial fireball to our telescopes, it picks up a lot of information about the gravitational fields of objects in between. One way this happens is through the bending of light, as discussed in Chapter 2. The background radiation is no exception to this phenomenon, and as it passes by massive objects, its trajectory is bent by their gravitational fields. This distorts the pattern of ripples in a calculable way. It changes what the ripples look like, and is an efect that was observed by Planck. Another efect that can be seen in the background radiation is due to the evolution of gravitational fields as the Universe expands. If this happens, then a photon that enters a gravitational field with a given amplitude could find itself leaving a field with a diferent amplitude. The diference in these amplitudes gives (or takes away) energy from the photon. Comparing observations of this efect to the theoretical predictions gives further evidence that the expansion of the Universe is speeding up.

  The expansion history

  After the Universe became cool enough to see through, there was a period that astronomers refer to as the dark ages. This was the period after the initial fireball, but before the first stars and galaxies formed. There is very little for astronomers to look at during this part of the Universe’s history, as most of the matter was in clouds of gas. After about a few hundred million years, however, the first stars and galaxies had begun to form. Since then, structures have grown continuously, and on ever larger scales, as the Universe has evolved. Of course it’s gravity that has caused this to happen, and much information can be obtained about gravity by looking at the astronomical structures around us. For the moment though, let’s think about how astrophysical bodies can be used to probe the expansion history of the Universe.

  Hubble started this field, with his famous paper in 1929. As with most great scientific results, his work was built upon and extended by the generations that followed. The aim of all this work has been to determine how fast a distant object is moving away from us, as well as exactly how far away from us that object is. This information can then be used to determine how fast the Universe is expanding. The former of these two problems is actually relatively straightforward. Light from stars, and most other bodies, is emitted in specific frequencies that correspond to the chemical elements that it’s made from. Now, when a body is in motion, as most astrophysical objects tend to be, then the frequency of the light that reaches us is shifted by the Doppler Efect. This phenomenon is the same as the shift in frequency you hear when an ambulance drives past you; the sound it emits seems higher pitched when it’s travelling towards you than when it’s moving away. In both cases, the change in frequency can be straightforwardly related to the velocity of the body in motion. This means that if we know the chemical elements in an astrophysical body (which we often do), then it’s relatively easy to work out how fast that body is moving away from us.

  Accurately determining the distance to astrophysical bodies is, however, a more challenging task. The general methodology that’s used for this job is to look at objects that are reasonably nearby. If we can determine the distance to these nearby objects, which is usually a bit easier, then we can use them to calibrate the distance to similar objects that are further away. As an example of this method, let’s consider the Cepheids that Hubble used in his famous paper. A Cepheid is a star whose brightness varies in a periodic way. It was already known that there is a relationship between the period of a Cepheid and its luminosity (its actual brightness, as opposed to its apparent brightness, which depends on distance from us). This was determined from nearby stars whose distances were known. Hubble used this information to work out the distance to faraway Cepheids. The logic is quite straightforward: you look at the Cepheid and measure its period; you use this information to work out how much light it’s emitting; and you compare this to how bright the object appears on your photographic plate. There’s a simple law that tells you how bright an object at a certain distance should be when it’s emitting a certain amount of light, so you have all the information you need to determine its distance.

  Unfortunately there are a number of things that can go wrong with this method. The rules used to determine the distance to an object (such as the relationship between period and brightness in Cepheids) might only be approximately true. You also have to assume that the distant objects observed are the same as the nearby objects that were used to determine the rule. This isn’t always true, as it can be hard to identify objects when they are very distant, and because it might be that some rules change over time (recall that when you look far away, you are looking at objects as they were long ago). These problems, and more, need to be carefully considered, as they can sometimes lead to incorrect inferences. In his 1929 paper, for example, Hubble inferred an expansion rate for the Universe that’s approximately ten times larger than all modern measurements. This error was due to incorrectly inferring the distances to galaxies using the Cepheids.

  The current state of the art in this field is achieved using observations of supernovae (exploding stars), but the underlying methodology is still quite similar to the one used by Hubble. An individual supernova can be as bright as an entire galaxy, so they are reasonably easy to spot, if you know what to look for. They can also be seen from very far away. Now, there are diferent ways that a supernova can happen, and, of course, astronomers have given names to them all. The type of supernovae that are most useful for probing the expansion of the Universe are known as Type Ia. These explosions are caused by the accretion of matter on to a white dwarf from a nearby star. When enough matter has accumulated, the white dwarf can no longer hold itself up against the pressure of gravity, and it collapses and explodes. The good thing about Type Ia supernovae is that they tend to happen in a very similar way, wherever or whenever they occur. This means that, if they can be properly identified, then their brightness can be used to get quite a good estimate of their distance.

  It wasn’t until the late 1990s that the first results on the expansion history of the Universe from Type Ia supernovae began to emerge.Both the Supernova Cosmology Project and the High-Z Supernova Search Team were working on this idea, and they published their first results at around the same time. Using observations of supernovae that were at vast distances, and hence that had exploded several billions of years ago, they found something very surprising. They determined that the expansion of the Universe was not slowing down, as one would expect for objects that fall away from each other under their mutual gravitational attraction, but was instead speeding up. This was entirely unexpected, and it shocked the physics community. In terms of our understanding of gravity, however, it’s especially fascinating. We』ll go into its consequences further in Chapter 6, but for now let’s return to the large-scale structure of the Universe.

  The late universe

  Just as stars group together to form galaxies, galaxies group together into structures called clusters and super-clusters. These are what cosmologists are referring to when they talk about large-scale structure. The study of the large-scale structure of the Universe, once again, was started by Hubble. It was Hubble who realized that the spiral-shaped objects that astronomers observed through their telescopes were, in fact, distant galaxies. Up until this point it had been a real question as to whether or not our own galaxy was the only one that existed in the Universe, like an island in the infinite cosmos. Using the Cepheids that we discussed earlier, Hubble showed that the spirals were much more distant than the stars we see around us. The only explanation was that they were larger bodies, themselves made up from very many stars. This started the quest to map the structures that exist around us.

  As with most branches of observational cosmology, progress in this new field was initially rather slow, and only began to pick up pace towards the end of the 20th century. One of the landmark missions in this field was the Harvard-Smithsonian CfA survey, which began in 1977 and ran until 1995. The CfA survey measured the recessional velocity of almost 20,000 galaxies, and recorded the position of each of them on the sky. Using Hubble’s law, they then converted these velocities into distances, and started to map out the structure that existed in the Universe on very large scales. They discovered that galaxies clump together to form structures that span enormous distance scales. One of the most impressive of these is what is known as the CfA2 Great Wall. This structure is a huge concentration of galaxies, which is so large it would take light more than half a billion years to get from one end to the other.

  More recent galaxy surveys have discovered even larger numbers of galaxies. The 2dF survey, which used the Anglo-Australia Telescope in New South Wales, ran from 1997 to 2002, and observed more than 200,000 galaxies. The Sloane Digital Sky Survey (SDSS), which started in the year 2000 and is planned to continue until 2020, has so far measured millions. In fact, there are now so many images of galaxies (and other astrophysical bodies) that it is impossible for astronomers to go through all of them individually. Computer programs can be used for this, but they tend to be worse at recognizing important features than the human eye (and brain). A clever way around this problem was therefore to put the images online and let the public take part in identifying them』a project known as 』Galaxy Zoo』.

  Many more structures were found by 2dF and SDSS, and on even larger scales than the CfA survey. The biggest of these was the Sloane Great Wall, which is around twice as big as the CfA2 Great Wall. In fact, the Sloane Great Wall is so big that if you took similar sized structures and put them end to end, you could only fit a few dozen in the entire observable Universe. It’s truly enormous, but one should bear in mind that this is still only a fraction of the distance probed by supernovae and the CMB. There are many more galaxies out there waiting to be discovered, and it remains to be seen if there are any structures that are even larger (the expectation is that there are not, but expectations are not always realized).

  This is all very impressive, but let’s return to what it means for the study of gravity. The structures that are observed in these surveys are the result of gravitational attraction. At very early times the Universe looked smooth, as verified by observations of the CMB. In order to get from that state to the present day situation, where there exists vast networks of structure, the matter in the Universe must have clumped together. The way in which this should happen is thought to be well understood on large scales, but starts to get a bit more complicated on small scales. Both of these regimes contain a wealth of information for those who are interested in gravity, so let’s consider them separately.

  On large scales the growth of structure happens in a predictable way. This is essentially because the large-scale bulk motion of the matter in the Universe is small on these scales when compared to the cosmological expansion. The growth of structure on large scales is, however, very sensitive to the precise rate of cosmological expansion. If the expansion is dominated by normal matter, then structures grow. This happens on smaller scales first, and on larger scales later on. Now, because we know what the seeds of structure look like, from the CMB, we can calculate what we expect the structure on large scales to look like, and we can compare this to what astronomers actually see. The results are very interesting.

  First, the results of observing structures on large scales indicates quite strongly that there is matter in the Universe that does not interact with light. The reason we know this is because there is more structure on certain length scales than there would be if this were not true. That is, if all matter interacted with light, then the high levels of radiation in the early Universe should have suppressed the seeds of structure in a predictable way. What we see, however, is the level of structure that one should expect if radiation hadn’t done this. The logical conclusion is that there exists matter in the Universe that does not interact with radiation, and that it was the gravitational field of this matter that served as the seeds of the structures that we see around us today. What is more, by looking at how much structure exists on diferent length scales, we can gain valuable information about how gravity works over very large distances.

  Second, the large-scale structure in the Universe can be used as a kind of ruler, to measure the size of the Universe and how much it has expanded. This is because the initial ripples have a characteristic length. By comparing the scale of these ripples in the background radiation, to the scales that occur in the large-scale structure around us, we can therefore see in quite a direct way how much the Universe has expanded (as the former is the source of the latter). This leads to yet another surprising result. The Universe seems to have expanded more than it should have done if its expansion were dominated by the gravitational field of the matter within it. In other words, the rulers in the late Universe seem to be too big.

  Let’s now consider what happens on smaller distance scales, much smaller than the great walls discussed earlier. On these scales the velocities of astrophysical bodies, like stars and galaxies, are not necessarily small compared to the cosmological expansion. The analysis is therefore much more complicated, as the bodies move and interact in much more complicated ways. The current best method for studying this situation is to create huge computer simulations of very many bodies. The space that the bodies exist within is expanding, as Einstein argued that it should, but the gravitational fields of the bodies within the space are usually treated in the way that Newton specified. This is a vast extrapolation of Newton’s ideas, but it is widely thought that it’s a valid way to proceed. Let’s now consider how gravity can be explored in this regime.

  The first and most obvious thing to do here is to track the motion of the galaxies, and the form of the larger structures that they create. This is very tricky, as it’s diicult to take into account all the complicated efects that can occur from the many astrophysical processes that take place in the Universe. A supernova, for example, could disrupt the growth of structure, or clouds of gas could enhance it. Nevertheless, one can try to model all such phenomena』and there has been a lot of progress in doing this since the turn of the century. What seems clear, as before, is that there appears to be a large amount of matter that we can’t see directly, but whose gravitational field is required to make galaxies move and cluster in the way they do.

  A second approach is to look at how galaxies, and clusters of galaxies, bend the path of light. You will recall that the Sun bends the path of starlight that passes close by it, and that this was how Eddington convinced the world that Einstein’s theory was correct. The same can be done with galaxies. We can look at how the shapes of distant galaxies are distorted by the gravitational fields of those that are much closer to us』in a process known as gravitational lensing. This efect is often very small, and it’s usually an enormous challenge to see it at all. If we look at the right galaxies, or collect enough data, however, then we can use it to determine the gravitational fields that exist in space. Once more, we find that there is more gravity than we expected there to be, from the astrophysical bodies that we can see directly. There appears to be a lot of mass, which bends light via its gravitational field, but that does not interact with the light in any other way. The exact amount of bending that occurs also potentially encodes a lot of information about the way that gravity behaves on the scales of galaxies, and clusters of galaxies.

  Moving to even smaller scales, we can look at how individual galaxies behave. It has been known since the 1970s that the rate at which galaxies rotate is too high. What I mean is that if the only source of gravity in a galaxy was the visible matter within it(mostly stars and gas), then any galaxy that rotated as fast as those we see around us would tear itself apart. It would be like taking a head of dandelion seeds and rotating its stem quickly between your hands. If you rotate it fast enough then you would expect the seeds to fly of, as the bonds that hold them together are not strong enough to resist the forces that result from the rotation. The same is true with the stars in galaxies. That they do not 』y apart, despite their rapid rotation, strongly suggests that the gravitational fields within them are larger than we initially suspected. Again, the logical conclusion is that there appears to be matter in galaxies that we cannot see but which contributes to the gravitational field.

  The concordance model

  Many of the diferent physical processes that occur in the Universe lead to the same surprising conclusion: the gravitational fields we infer, by looking at the Universe around us, require there to be more matter than we can see with our telescopes. Beyond this, in order for the largest structures in the Universe to have evolved into their current state, and in order for the seeds of these structures to look the way they do in the CMB, this new matter cannot be allowed to interact with light at all (or, at most, interact only very weakly). This means that not only do we not see this matter, but that it cannot be seen at all using light, because light is required to pass straight through it.

  This is obviously a very strange state of afairs. The substance that gravitates in this way but cannot be seen is referred to as dark matter. The amount of dark matter required to explain the observations is not small. There needs to be approximately five times as much dark matter as there is ordinary matter. Most people, when they first hear this news, think something must have gone terribly wrong. That nature cannot be this strange. Yet, the evidence for the existence of dark matter comes from so many diferent sources that it is hard to argue with it. If the evidence only came from one place, you could try and make a case that whoever collected the data, or made the observations, might have made a mistake. It’s very diicult, though, to make this argument for all of the diferent types of observations listed here. To make so many mistakes, and for all those mistakes to conspire to suggest the same result, seems highly unlikely. So we are led to the conclusion that most of the matter in the Universe is not of the type with which we are most familiar, but is instead some new type of matter that was previously unknown.

  But this is not the end of the surprises. Not only do we require extra matter to give extra gravitational fields in order to make structures form and light bend in the way that it’s observed to do, but we also have to explain why the Universe is expanding faster than we thought it should. Recall that we can think of the expansion of the Universe as objects made of matter (such as galaxies) 』ying away from each other under their mutual gravitational interaction. If this is true, and if gravity is always attractive, then we should expect the large-scale expansion of the Universe to be always decelerating. That is, the expansion should be getting slower over time. The results of the various astronomical observations we have discussed, however, have shown that the expansion is speeding up. The conclusion is that there must be a type of gravitational field that is repulsive』in other words, there seems to be a type of anti-gravity at work when we look at how the Universe expands. This anti-gravity is required in order to force matter apart, rather than pull it together, so that the expansion of the Universe can accelerate. This is truly astonishing. The source of this repulsive gravity is referred to by scientists as dark energy (not to be confused with dark matter). There needs to be around three times as much dark energy as there is dark matter, in order to make the Universe accelerate in its expansion at the current rate.