Cosmology_A Very Short Introduction

by Peter Coles

  New technology has enabled astronomers to search (and find) Type Ia in galaxies with redshifts around one. (Remember that this means that the Universe has expanded by a factor of two while light has been travelling from the supernova to us.) Comparing the observed brightness of the distant supernova with nearby ones can give an estimate of how much further away they are. This, in turn, tells us how much the Universe has been slowing down in the time taken for the light to reach us. The trouble is that these supernovae are fainter than they should be if the Universe is slowing down. The Universe is not decelerating at all, but speeding up.

  This observation strikes at the heart of the standard description of cosmology embodied in the Friedmann equations. All these models should be decelerating. Even the members of the Friedmann family with low Ω, whose deceleration is only slight owing to their low density, should not be speeding up. And the models with critical density apparently favoured by inflation should undergo heavy deceleration. What has gone wrong?

  Einstein’s biggest wonder?

  The supernova observations I’ve been talking about are still controversial, but they certainly seem to indicate that a dramatic change in cosmological theory is needed. On the other hand, there is an off-the-shelf remedy for this bug that dates from Einstein himself. In Chapter 3 I mentioned how Einstein altered his original theory of gravitation by introducing a cosmological constant. His reason for doing this, an act he later regretted, was that he wanted to make a theory that could describe a static (i.e. non-expanding) universe. His cosmological constant altered the law of gravity to prevent space from either expanding or contracting. Applied in the modern context, the cosmological constant can be introduced to make the law of gravity repulsive on large scales. If this is done, the tendency of the gravitational attraction of matter to slow down the Universe is overwhelmed by a cosmic repulsion that causes it to speed up.

  This cure of course requires one to accept that the cosmological constant wasn’t a bad idea in the first place. But modern theory also gives us a new understanding of how this can happen. In Einstein’s original theory, the cosmological constant appeared in the mathematical equations describing gravity and space-time curvature. It was indeed a modification of the law of gravity. But he could just as easily have written this term on the other side of his equations, in the part of the theory that describes matter. Over on the other side of Einstein’s equations, his infamous cosmological constant appears as a term describing the energy density of the vacuum. A vacuum that has energy may sound strange, but we have come across it before in this chapter. It is exactly what is needed to cause inflation.

  In the early versions of cosmic inflation theory, the vacuum energy liberated by a primordial phase transition disappears after the transient period of hyper-expansion is over. But maybe a small amount of this energy survived until now and it is this energy that has made gravity push instead of pull. The idea that this vacuum energy may be causing the acceleration also allows us to reconcile the theory of inflation with the evidence that Ω may be significantly less than the unit value it would have to have if space were flat. While the vacuum energy is perverse in that it makes gravity push rather than pull, it does at least curve space in the same way that ordinary matter does. If we have a Universe with both matter and vacuum energy then we can have flat space without the deceleration that is required in an ordinary Friedmann model.

  We still don’t really know for sure whether the Universe is accelerating, whether there is a vacuum energy, or what precisely is the value of Ω. But these ideas have provoked intense activity over the last few years in both theory and experiment. And there is a new generation of measurements coming along that could, if they work, answer all these questions. I’ll discuss these in the next chapter.

  Chapter 7

  Cosmic structures

  Galaxies are the basic building blocks of the Universe. They are not, however, the largest structures one can see. They tend not to be isolated, but like to band together rather like people. The term used to describe the way galaxies are distributed over cosmological distances is large-scale structure. The origin of this structure is one of the hot topics of modern cosmology but, before explaining why this is so, it is first necessary to describe what the structure actually is.

  Patterns in space

  The distribution of matter on large scales is usually determined by means of spectroscopic surveys that use Hubble’s Law to estimate the distances to galaxies from their redshifts. The existence of structure was known for many years before redshift surveys became practicable. The distribution of galaxies on the sky is highly non-uniform, as can be seen in the first large systematic survey of galaxy positions which resulted in the Lick Map. But impressive though this map undoubtedly is, one cannot be sure if the structures seen in it are real, physical structures or just chance projection effects. After all, we all recognize the constellations, but these are not physical associations. The stars in them lie at very different distances from the Sun. For this reason, the principal tool of cosmography has become the redshift survey.

  20. The Andromeda Nebula. The nearest large spiral galaxy to the Milky Way, Andromeda is a good example of its type. Not all galaxies are spiral; rich clusters like Coma contain mainly elliptical galaxies with no spiral arms.

  A famous example of this approach is the Harvard-Smithsonian Center for Astrophysics (CfA) survey, which published its first results in 1986. This was a survey of the redshifts of 1,061 galaxies found in a narrow strip on the sky in the original Palomar Sky Survey published in 1961. This survey has subsequently been extended to several more strips by the same team. Until the 1990s redshift surveys were slow and laborious because it was necessary to point a telescope at each galaxy in turn, take a spectrum, calculate the redshift and then move to the next galaxy. To acquire several thousands of redshifts took months of telescope time, which, because of the competition for resources, would usually be spread over several years. More recently the invention of multi-fibre devices on wide-field telescopes has allowed astronomers to capture as many as 400 spectra in one pointing of the telescope. Among the latest generation of redshift surveys is one called the Two-Degree Field (2dF) survey, run by the United Kingdom and Australia using the Anglo-Australian Telescope. This will eventually map the positions of around 250,000 galaxies.

  21. The Lick Map. Produced by meticulous eyeball counting of galaxies on survey plates, the Lick Map displays the distribution of about a million galaxies over the sky. The pattern of filaments and clusters is impressive; the dense round lump near the centre is the Coma cluster.

  The general term used to describe a physical aggregation of many galaxies is a cluster of galaxies, or galaxy cluster. Clusters can be systems of greatly varying size and richness. For example, our galaxy, the Milky Way, is a member of the so-called Local Group of galaxies, which is a rather small cluster of galaxies of which the only other large member is the Andromeda galaxy (M31). At the other extreme, there are the so-called rich clusters of galaxies, also known as Abell clusters, which contain many hundreds or even thousands of galaxies in a region just a few million light years across: prominent nearby examples of such entities are the Virgo and Coma clusters. In between these two extremes, galaxies appear to be distributed in systems of varying density in a roughly fractal (or hierarchical) manner. The densest Abell clusters are clearly collapsed objects held together in equilibrium by their own self-gravity. The less rich and more spatially extended systems may not be bound in this way, but may simply reflect a general statistical tendency of galaxies to clump together.

  Individual galaxy clusters are still not the largest structures to be seen. The distribution of galaxies on scales larger than around 30 million light years also reveals a wealth of complexity. Recent observational surveys have shown that galaxies are not simply distributed in quasi-spherical ‘blobs’, like the Abell clusters, but also sometimes lie in extended quasi-linear structures called filaments, or flattened sheet-like structures such a
s the Great Wall. This is a roughly two-dimensional concentration of galaxies, discovered in 1988 by astronomers from the Harvard-Smithsonian Center for Astrophysics. The Great Wall is at least 200 million light years by 600 million light years in size, but is less than 20 million light years thick. It contains many thousands of galaxies and has a mass of at least 1016 solar masses. The rich clusters themselves are clustered into enormous loosely bound agglomerations called superclusters. Many are known, containing anything from around ten rich clusters to more than fifty. The most prominent known supercluster is called the Shapley concentration, while the nearest is the Local Supercluster, centred on the Virgo cluster mentioned above, a flattened structure in the plane of which the Local Group is moving. Superclusters are known with sizes as large as 300 million light years, containing as much as 1017 solar masses of material.

  These structures are complemented by vast nearly empty regions, many of which appear to be roughly spherical. These ‘voids’ contain very many fewer galaxies than average, or even no galaxies at all. Voids with

  22. The 2dF galaxy redshift survey. This survey, which is still in progress, is planned to measure the redshifts of around 250,000 galaxies. Although parts of the survey are not finished, resulting in missing pieces of the map, one can see the emergence of a complex network of structures extending out to billions of light years from us.

  density less than 10 per cent of the average density on scales of up to 200 million light years have been detected in large-scale redshift surveys. The existence of large voids is not surprising, given the existence of clusters of galaxies and superclusters on very large scales, because it is necessary to create regions of less than average density for there to be regions of greater than average density.

  The impression one has when looking at maps of large-scale structure is that of a vast cosmic ‘web’, a complex network of intersecting chains and sheets. But how did this complexity arise? The Big Bang model is predicated on the assumption that the Universe is smooth and featureless, i.e. that it conforms to the Cosmological Principle. Fortunately the structure does indeed seem to peter out on scales larger than the scale of the cosmic mesh. This is also confirmed by observations of the cosmic microwave background, which comes to us after travelling about 15 billion light years from the early Universe. The microwave background is almost uniform on the sky, consistent with the Cosmological Principle. Almost, that is, but not quite.

  Structure formation

  In 1992, the COBE satellite deployed its sensitive detectors to the task of detecting and mapping any variation in the temperature of the microwave background on the sky. At its discovery in 1965 the microwave background seemed to be isotropic on the sky. Later it was found that it had a large-scale variation across the sky of about one part in a thousand of the temperature. This is now known to be a Doppler effect, caused by the Earth’s motion through the radiation field left over from the Big Bang. The sky looks slightly warmer in the direction we are heading, and slightly cooler in the direction we are coming from. But aside from this ‘dipole’ variation (as it is called), the radiation seemed to be coming equally from all directions. But theorists had suspected for a long time that there should be structure in the microwave background, in the form of a ripply pattern of hot and cold splotches. It was these that COBE found, and in so doing, caused newspaper headlines around the world.

  So why is the microwave background not smooth after all? The answer is intimately connected to the origin of large-scale structure and, as ever in cosmology, gravity provides the connection.

  Friedmann’s models provide important insights into how the bulk properties of the Universe change with time. But they are unrealistic because they describe an idealized world that is perfectly smooth and blemish-free. A Universe that starts out like that will remain perfect forever. In a realistic situation, however, there are always imperfections. Some regions may be slightly denser than average, some more rarefied. How does a slightly lumpy Universe behave? The answer is dramatically different to the idealized case. A piece of the Universe that is denser than average exerts a stronger gravitational pull on its surroundings than average. It will therefore tend to suck material in, depleting its neighbourhood. In the process it gets even denser relative to the average, and pulls still harder. The effect is a runaway growth of lumpiness called the ‘gravitational instability’. Eventually strongly bound lumps form and begin to collect into filaments and sheets resembling those seen in maps of cosmic structure. Only very slight fluctuations are needed to kick the process off, but gravity acts like a powerful amplifier transforming minute initial ripples into huge fluctuations in density. We can map the end product using galaxy surveys; we see the initial input in the COBE map. We even have a good theory of how the initial fluctuations imprinted; cosmic inflation produces quantum fluctuations.

  The basic picture of how structure forms has been around for many years, but it is hard to turn this into detailed predictive calculations because of the complicated behaviour of gravity. I mentioned in Chapter 3 that even Newton’s laws of motion are difficult to solve without simplifying symmetry. In the late stages of gravitational instability, there is no such simplification. Everything in the Universe pulls on everything else; it is necessary to keep track of all the forces acting everywhere and on everything. The sums involved are just too hard to be solved with pencil and paper.

  23. The COBE ripples. In 1992 the Cosmic Background Explorer (COBE) satellite measured slight fluctuations of about one part in 100,000 of the temperature of the cosmic microwave background on the sky. These ‘ripples’ are thought to be the seeds from which galaxies and large-scale structure grew.

  During the 1980s, however, massive computers came on the scene, and progress in the field accelerated. It became obvious that gravity could form cosmic structure but in order for it to do the job effectively there would have to be quite a lot of mass in the Universe. Because only a relatively small amount of ‘normal’ matter is allowed by primordial nucleosynthesis arguments, theorists assumed the Universe to be dominated by some form of exotic dark matter that does not involve itself in nuclear reactions. Simulations showed that the best form of matter for this was ‘cold’ dark matter. If the dark matter were ‘hot’ then it would be moving too quickly to form clumps of the right size.

  Eventually, after many years of computer time, a picture emerged in which cosmic structure arises in a bottom-up fashion. First, small clumps of dark matter form. These building blocks then coalesce into larger units, which then themselves coalesce, and so on. Eventually objects the size of galaxies form. Gas (which is made of baryonic material) falls in, stars form, and we have galaxies. The galaxies continue the hierarchical growth of structure by clustering in chains and sheets. In this picture, structure evolves rapidly with time (or, equivalently, with redshift).

  24. The Hubble deep field. Made by pointing the Hubble Space Telescope at a blank piece of sky, this image shows a wonderful array of distant faint galaxies. Some of these objects are at such enormous distances that light has taken more than 90 per cent of the age of the Universe to reach us. We can therefore see galaxy evolution happening.

  The idea of cold dark matter has been very successful, but this programme is far from complete. It is still not known how much dark matter there is, nor what form it takes. The detailed problem of how galaxies form is also unsolved because of the complex hydrodynamical and radiative processes involved with the motion of gas and the formation of stars. But now this field is not just about theory and simulations. Breakthroughs in observational technology, such as the Hubble Space Telescope, now allow us to see galaxies at high redshift and thus study precisely how their properties and distribution in space has changed with time. With the next generation of huge redshift surveys we will have enormously detailed information about the pattern that galaxies trace out in space. This too holds clues as to how much dark matter there is, and precisely how galaxies formed. But the final resolution of this problem is likely to co
me not from observations of the end product of the gravitational instability process but at its beginning.

  The sound of creation

  The COBE satellite represented an enormous advance in the study of structure formation, but in many ways this experiment was very limited. The most important shortcoming of COBE was that it lacked the ability to resolve the detailed structure of the ripples in the microwave background. In fact COBE’s angular resolution was only about ten degrees, which is very crude by astronomical standards. The full Moon, for comparison, is about half a degree across. It is in the fine structure of the microwave sky that cosmologists hope to find the answers to many outstanding questions.