Chapter 1 The runaway galaxies - Life in a puzzling universe



Chapter 5 Big Bang ParametersThis chapter describes the advent of observational cosmology and the search for the main parameters of the big bang model. We then consider the emergence of several big bang puzzles and the problem of fine tuning By the 1970s, cosmology had finally become a major research area in physics. There were now four main planks of evidence for the big bang model; the recession of the galaxies (Hubble’s law), the abundance of the lightest elements, the distribution of the radio galaxies and the cosmic microwave background. However, all of this evidence was rather qualitative and a new generation of physicists took on the task of establishing quantitative parameters of the model. The search for two numbersOne problem with the big bang model is that the relativistic models of Friedmann and Lema?tre describe evolving universes in general; they do not specify which type of universe we live in. Key parameters are not predicted by the model, but are determined by observation. In particular, the two most important variables - the rate of expansion of the universe and the density of matter - are not specified. We recall from chapter 2 that both the fate and the geometry of the universe are decided by a competition between these two parameters1. If the initial density of matter in the universe is below a certain critical value, the expansion of the universe will overcome the pull of gravity and expand forever (with the open geometry shown in figure 5): if the matter density is above this value, gravity eventually overcomes the expansion (and the universe will exhibit closed geometry). In between these cases lies the special case of a universe with an exact balance between expansion and gravity (flat geometry).This is one reason one talks about models of the expanding universe; it was realised early on that these two parameters could only be determined by observation2.Fig 5 Three possibilities for the universe depending on the initial values of the rate of expansion versus the density of matter The search for the Hubble constantConsidering the rate of expansion first, it can in principle be estimated directly from the Hubble constant H0 , i.e. from the slope of the velocity-distance graph of the galaxies (figure 5). Unfortunately, this parameter is very sensitive to errors in our estimates of the absolute distances to the stars, as we saw in chapter 4. From the 1970s onwards, astronomer devoted a great deal of time and energy to the determination of a reliable scale for stellar distance3. A key player in this program was Allan Sandage, Baade’s successor at the Mount Wilson observatory. Working with a 200-inch Palomar telescope, Sandage approached the problem using a variety of methods, putting particular emphasis on obtaining extremely accurate measurements to the nearest galaxy clusters. However, a serious dispute arose between his estimate of H0 and that of a group led by Gerard de Vaucouleurs at the McDonald observatory of the University of Texas. This debate lasted right up until the 1990s, with the Hubble Space Telescope providing a definitive answer midway between the two estimates4. The search for the density of matter As regards the density of matter in the universe, we recall first that it is specified in the Friedmann models in terms of the parameter Ω, the ratio of the actual density to the critical density required to close the universe5. The critical density can be calculated from theory (although it depends on the Hubble constant, as you might expect), but how does one determine the actual density of matter at any epoch? A first guess comes from calculations of primordial nucleosynthesis (chapter 3). In order to accurately predict the observed abundances of the lightest elements, the calculations must assume a value for the matter density that is very low (Ω ~ 0.3) relative to the critical value (Ω = 1). This value implies a universe that easily overcomes the pull of gravity. However, this method is very limited as it considers only baryonic matter i.e. particles that take part in nuclear reactions (protons and neutrons). Nucleosynthesis puts no limit on the amount of non-baryonic matter in the universe and such matter could contribute significantly to the mass of the universe.A second method is to estimate the mass of all the observable galaxies and galaxy clusters; this is done by measuring their gravitational effects on other bodies6. These measurements offered support for a surprising idea that had been around for some time; there appears to be a great deal of matter in the universe that is observable only by its gravitational effect. For example, measurements of the speed of rotation of certain galaxies strongly suggest the presence of nearby matter that is not detectable through telescopes at any wavelength. Such matter is called dark matter and its existence was first mooted by the Swiss astronomer Fritz Zwicky in the 1930s. Although dark matter was seen as something of a fudge for some years, the phenomenon is now accepted by the vast majority of cosmologists7. That said, the nature of the particles that make up dark matter remains unknown8. We shall return to this topic many times - for the moment, we note that, even including the contribution of dark matter, the ‘gravitational method’ suggested a density value of about Ω = 0.2 for today’s universe, again indicating an expanding universe that overcomes the pull of gravity.A third method is to use very distant objects to measure the curvature of space (recall that this curvature is directly related to mass, according to relativity). Such methods also suggested a value of Ω less than 1, but they turned out to be rather error-prone. Yet another method is to measure the luminosity of galaxies and convert this to a measurement of mass density using an estimate of the mass-to-light ratio of matter. This is a rather complicated method9 and we simply note that such measurements suggested a value of Ω = 0.25. All in all, the various observational methods seemed to indicate a value of Ω between 0.1 and 0.3, indicative of an open universe. But where did this value come from? What property of the early universe resulted in a value of Ω ~ 0.3?The problem of structureAnother question soon emerged; how did large-scale structures such as galaxies and galaxy clusters form? The Friedmann/Lema?tre models presume a universe that is both isotropic and homogenous on the largest scales. As astronomy progressed in the 1960s and 70s, this principle seemed to be supported more and more by observation. On the other hand, the density of matter in a particular galaxy is approximately one million times the density in the cosmos at large. How did this happen? The obvious approach in the study of the formation of the galaxies is to assume that natural infinitesimal fluctuations in the density of the early universe were amplified by the force of gravity, becoming the structures we see today. However, early calculations by Lema?tre, Richrad Tolman and Evgenii Lifshitz showed that, in an expanding universe, such fluctuations are too small to give rise to the large-scale structures observed today 10. Hence, one must assume that the universe was ‘born’ with irregularities of just the right size to give rise to the galaxies we see today.In the 1960s,Yakov Zeldovitch and Igor Novikov of Moscow University, and Jim Peebles of Princeton, re-examined this question in the context of measurements of the cosmic microwave background. As we saw earlier, the background radiation is a snapshot of the universe at the time when free particles coalesced into atoms (the epoch of recombination, long before the formation of galaxies). Fluctuations in density existing at that time were imprinted on the cosmic background radiation, measurable today as tiny fluctuations in the temperature of the radiation. From these considerations, two competing models of galaxy formation arose – a bottom-up process where the initial perturbations in the primordial plasma simply grew larger and larger to form galaxies (Peebles et al) and a top-down process, where the initial perturbations clumped to form large growths of matter which later fragmented into galaxies (Zelowitch et al). However, neither model was very successful11.Another approach concerned neutrinos. The lightest known particles, neutrinos travel almost at the speed of light and are extremely weakly interacting. The number of neutrinos in the universe is not constrained by nucleosynthesis calculations because they do not partake in nuclear reactions (see above). Hence a universe filled with enough neutrinos could give rise to the density fluctuations necessary for the formation of galaxies; this theory became known as the hot dark matter model of galaxy formation. However, the model fell out of favour when measurements in particle accelerators showed that neutrinos are simply too light to play a major role in galaxy formation 12.A final possibility was cold dark matter. In this scenario, dark matter particles that are heavier and slower than neutrinos might provide a mechanism for the formation of galaxies. In 1982, Jim Peebles showed that this hypothesis could indeed produce the measured fluctuations in the cosmic microwave background13. To this day, the hypothesis of cold dark matter predicts a spectrum for the microwave background that is in good accord with measurements from satellite telescopes , as we shall see in chapter seven. Unfortunately, the model does not specify the nature of the particles making up the cold dark matter!The problem of baryon numberAnother puzzle concerned the number of baryons in the universe (recall that a baryon is the name given to particles that partake in nuclear reactions i.e. protons and neutrons). In the big bang model, one expects the total number of baryons in the universe to remain constant as the universe expands14. One also expects the number of photons (the particles that make up radiation) to remain constant. Hence the ratio of baryons to photons is a characteristic parameter that was fixed early in our universe – and in fact is measured as about 1 billion photons for every baryon. But what determined this ratio? Was the universe born with this characteristic?The problem of fine tuningAll of the parameters above share an important feature; they are not predicted by the Friedmann-Lema?tre models, but have to be assumed. This is known as the problem of initial conditions or the fine tuning problem. Why should the Hubble constant have the value it does? What determined the initial value of the density of matter? What determined the ratio of photons to baryons? What caused the fluctuations in matter density that gave rise to today’s galaxies? While the four planks of evidence for the big bang model stood on solid ground, it was unsatisfactory that so many parameters of the model had to be assumed, rather than be predicted by the theory. This led some to wonder whether the model was incomplete; and an old puzzle lent weight to this idea.The problem of the singularityA final big bang puzzle was the old conundrum of the singularity. As we saw in chapter 3, backtracking along the Friedmann-Lema?tre graphs brings one to a universe that is infinitely small and infinitely dense, which seems rather unreasonable. The big bang universe does not make sense at ‘time zero’! This problem was sidelined for some years – after all, it is not unusual for perfectly good theories to break down at some point (note that Newtonian gravity also contains a singularity14). It is interesting that Einstein himself warned of the dangers of extrapolating relativistic models back to a universe of atomic dimensions. However, in the 1970s, Stephen Hawking and Roger Penrose published a number of theorems suggesting that an expanding universe must begin in a singularity, assuming only very general conditions15. This development brought the problem of the singularity once more to the fore.How does one resolve the puzzle of the singularity? The key undoubtedly lies in the realm of quantum physics. The Friedmann-Lema?tre model is rooted in general relativity, a theory that takes no account of quantum effects – yet one can certainly expect quantum effects to become important in a universe of atomic dimensions16. Hence we cannot expect to have a reliable description of the origin of the universe until we have a version of general relativity that incorporates quantum physics. Much effort has been devoted to achieving this synthesis but it has proved elusive. It is a remarkable fact that the two great pillars of modern physics, general relativity and quantum physics, have so far proved irreconcilable. One consequence of this failed marriage is that the big bang model is an effective model, not a complete one. We note once more that the moniker ‘big bang’ is a terrible misnomer as the model breaks down long before a ‘bang’ is reached. That said, we shall see in the next chapter that a radical new version of the theory was to cast some light on this great puzzle…Chapter 6 The inflationary universeIn this chapter, we encounter two major puzzles associated with the big bang model, the so-called horizon and flatness problems. We see how a new version of the big bang model, the theory of cosmic inflation, addresses these problems and offers a new insight into the formation of the galaxies We saw in the last chapter that despite its great successes, a shortcoming of the big bang model is that many parameters are not specified by the model, and one must assume the universe was ‘born’ with certain characteristics such as the Hubble constant, the initial density of matter and the baryon-to-photon ratio. As theorists analysed the model further, some puzzles of a more fundamental nature emerged, notably the horizon and flatness problems. The horizon problemOne outstanding puzzle concerned the homogeneity of the universe. We recall that the Friedmann-Lema?tre models assume that the universe is both isotropic and homogeneous on the largest scales (the cosmological principle). As astronomy progressed in the 1960s and 70s, this assumption was increasingly supported by observation. The Hubble expansion appeared to be the same in every direction. Galaxy surveys also revealed a large-scale uniformity; for any given epoch, the density of galaxies and galaxy clusters appeared to be approximately constant. Most tellingly, there seemed to be no detectable variation in the intensity of the cosmic background radiation, suggesting a high degree of homogeneity in the universe at the time of the formation of atoms. As studies of the cosmic microwave background progressed, it became increasingly clear that the radiation was extremely smooth, indicating an extremely homogeneous universe at least at the time of recombination.1Unfortunately, it was not clear why the universe should be so homogeneous. In nature, such equilibrium is only achieved by objects coming into thermal contact with one another and exchanging energy until any inhomogeneities are balanced out (just as a hot cup of tea eventually cools to the temperature of its environment). However, calculations show that the most distant regions of our universe could not have been in such causal contact; there simply hasn’t been enough time for light to travel from one such region to another during the lifetime of the universe. The limit of influence any section of space is set by the finite speed of light and is called its horizon; hence this paradox is known as the horizon problem. Simply put, the smoothness of the microwave background suggests that regions of the universe separated by distances far greater than their respective horizons have nonetheless been in thermal contact.You might argue that no such paradox should apply in a universe that originated in a minute volume of space; surely all regions were originally in thermal contact? In a way this is correct. The problem is one of backtracking, as we try to reconcile the homogeneity of today’s universe with both its scale and its age. One way of thinking about the horizon problem is that the size of the universe, as measured from the Hubble graph, doesn’t seem to match its contents.The flatness problem Another puzzle concerned the geometry of the universe. As we saw earlier, relativity predicts that the curvature of the universe is determined by the density of matter within it; in an expanding universe, the density of matter decreases over time and hence the density parameter Ω also evolves (recall that Ω is the ratio of the actual density of matter to the critical value required to close the universe). A careful analysis of the behaviour of this parameter over time led the Princeton physicist Robert Dicke to a startling prediction; if the density of matter diverged from the critical value (Ω = 1) by even a minute amount in the first fractions of a second, this divergence would accelerate rapidly with time, resulting in either a runaway closed or a runaway open universe 1(see figure 8).? Since observations suggest that we live in neither of these, Dicke’s analysis forces us to conclude that the density of matter in the infant universe must have been extremely close to the critical value. However, this conclusion was problematic. First, how could it be reconciled with the observational value of ? ~ 0.3 (see last chapter)? Second, it seems extraordinary that the infant universe should be so delicately balanced between the energy of gravity and the energy of expansion. This conundrum became known as the flatness problem.Figure 8; The flatness problem; calculations show that the slightest deviation from flatness in a universe 1 nanosecond old quickly amplifies, resulting in a runaway closed or runaway open universe. The theory of inflationIn the early 1980s, a new version of the big bang model was proposed. This model arose from considerations in particle physics and marked the beginning of an extremely fruitful alliance between the fields of sub-atomic physics (the world of the extremely small) and cosmology (the world of the extremely large). The core of the proposal was simple but startling; what if, during the first fractions of a second, the infant universe underwent a dramatic, exponential expansion of space, after which it relaxed to the slower expansion we measure today?2 This idea is associated with the American particle physicist Alan Guth and he named his proposal the inflationary universe . What could cause the infant universe to undergo a rapid expansion in the first fractions of an instant? Guth postulated that, as the nascent universe cooled, it may have been trapped in an energy state known as a false vacuum; the latter is a ‘metastable’ state of high energy density that is temporarily prevented from relaxing to the natural or ‘ground’ state of lowest energy. (A good analogy is a marble sitting on top of an inverted bowl: the marble is stable, but will easily fall to a lower energy state if nudged). An important property of the false vacuum is that it exerts a negative pressure on its surroundings, not unlike suction. Now pressure, according to general relativity, has an associated gravitational field; in particular negative pressure creates a repulsive gravitational field. Hence, a false vacuum state could create a significant force of repulsion.The idea of a universe that expands exponentially was not entirely new (it arises in the context of the de Sitter model and more modern versions were proposed by Andrei Linde , Yakov Zeldovich, Alexei Starobinsky and others4); however, Guth’s key insight was that an exponential expansion of the infant universe could offer a simultaneous solution to the horizon and flatness problems5. Inflation and the horizon problemFor the case of the horizon problem, we imagine a minute6 patch of space before inflation begins; a uniform, homogeneous state is easily established in such a region because all points are in thermal contact. When inflation occurs, this region of space is stretched exponentially; neighbouring points are driven apart to distances so large they cannot communicate even by light signals. In the language of physics, the components of the region are swept far beyond their particle horizons by inflation (recall that the horizon of each component is set by the finite speed of light). The homogeneity of the region is preserved, although it will appear quite mysterious to an observer! (see figure 10). Figure 10 If a minute, homgeneous region of space is stretched to a size larger than today’s observable universe, its homogeneity is preserved But surely the rate of expansion of the early universe is constrained by the speed of light? In fact, relativity specifies the speed of light in vacuum as a limiting speed for any object in spacetime ; it sets no limits on the behaviour of space itself. Thus, it is possible in principle for the expansion of space to be arbitrarily large. Indeed, according to inflation, a small region of space could have been inflated to dimensions larger than the universe we observe today. This aspect of inflation forces one to consider that the universe we measure may simply be the observable universe - a small patch of a much larger entity!Inflation and the flatness problemThe concept of inflation also offered a neat solution to Dicke’s flatness problem. If a region of space is inflated in the first fractions of an instant to a size larger than the universe we observe, its geometry will inevitably appear flat to us, just as the surface of an enormous balloon appears flat to an insect on it. This solves the flatness paradox beautifully; instead of deviations from flatness leading quickly to either a runaway open or runaway closed universe, inflation posits a universe that is driven towards flatness (see figure 10). Hence, the theory makes a very clear prediction; the geometry of the observable universe should be exactly flat, to a high degree of accuracy (more on this in chapter 7). Figure 10 Inflation drives the infant universe towards flatness In sum, inflation pushes the universe into a remarkably simple state, since all inhomogeneities and local curvatures of space are smoothed out by the enormous expansion; such a universe is nowadays called a no-hair universe7. New inflationGuth’s paper on inflation was ‘a shot around the world’, not least because he emphasized how the model offered an intriguing solution to both the horizon and flatness problems. However, it was clear from the outset that it contained a significant flaw. The theory could not describe how inflation ends, relaxing to the familiar Hubble expansion (Guth initially postulated that the universe got out of its metastable state by a process of quantum tunnelling,8 but calculations showed that this process gives rise to huge inhomogeneities not observed in today’s universe). This problem became known as the graceful exit problem. The problem was overcome in 1982, when the Russian theorist Andrei Linde and the American physicists Paul Steinhardt and Andy Albrecht independently published new versions of the inflationary universe9. In these models, the false vacuum state is less severe than that of Guth and the phase transition to the state of lowest energy is a much gentler process (figure 12). These models solved the graceful exit problem and became known as new inflation. It’s worth noting that new inflation did not specify a particular quantum field, simply that the field should have an extremely flat potential energy and a slow transition to the true vacuum10. New inflation also gave a good description of the important phenomenon of reheating. During the garangtuan expansion, one can expect that the universe underwent a tremendous cooling.The new inflation models described an exit from the false vacuum state that resulted in a huge release of energy in the form of incredibly hot radiation and particles, exactly the ‘initial state’ required by traditional big bang models. But the best was yet to come...Figure 12: New and old models of inflationA mechanism for galaxy formationMany cosmologists were struck by the way inflation simultaneously addressed both the horizon and flatnesss problems. With the problem of the ending of inflation being cleared up, they became interested in inflation as a potential mechanism for galaxy formation .As we saw earlier, quantum physics predicts minute variations in the density of matter in the infant universe. 11 However, detailed studies of galaxy formation had long suggested that such perturbations were simply too small to give rise to the large-scale structures of today. Hence, one was forced to assume that the universe was ‘born’ with certain inhomogeneities. Inflation breathed new life into this question; with the aid of an exponential expansion during the first fractions of a second, could natural fluctuations in density have given rise to the galaxies after all?A feverish amount of calculation followed, with analyses by Guth, Linde, Steinhardt, Hawking, Micheal Turner and many others. (A key stepping stone was to see whether quantum perturbations in an inflationary universe could give rise to the inhomogeneites in the cosmic background radiation necessary for the seeding of the galaxies). After several false starts, a great deal of thought and three weeks of hard calculation at a workshop in Cambridge University12, a stunning result was announced - natural fluctuations in density in an inflationary universe could indeed give rise to the perturbations responsible for today’s large scale structures!13. This was an exciting advance – a theory that was posited to address the horizon and flatness problems had given the first working explanation for the seeding of the galaxies. Best of all, the explanation arose from fundamental considerations of quantum physics, opening up a new area of research – the synthesis of quantum theory, particle physics and cosmology, a thriving field now known as particle cosmology. As we shall see in the next chapter, increasingly precise measurements of the cosmic microwave background were to offer further support for the analysis.Inflation and the philosophy of scienceIt is often stated that the theory of inflation constituted a new paradigm in cosmology. However, it is probably more accurate to say that it is an intriguing addition to the existing big bang paradigm. After all, the theory simply superimposes an extremely brief period of hyper-expansion on traditional models of the expanding universe. Inflation is therefore a variant on the big bang model, a version of the theory that provides a natural explanation for several ‘coincidences’ that are otherwise hard to explain – the homogeneity of the universe, its geometry and its large-scale structure (we shall see in chapter 7 that more accurate measurements of all three of these parameters offer further support for the theory). These are no mean accomplishments - scientists are always impressed by a theory that can explain apparently special conditions in terms of general considerations. However, it should be noted that some physicists find the theory of inflation rather contrived. Is it reasonable to be talking about unimaginably large expansions of space (of the order of 1050) ocurring over unimaginably short timespans (of the order of 10 -30 s)? It seems rather speculative and divorced from reality. How could such a theory ever be tested directly?A more specific problem concerns the mechanism of inflation. To this day, it is not known what type of physical field could give rise to the phenomenon. A great many models of inflation have emerged and it is not clear how to decide between them – this is not a situation physicists enjoy . There is also a new problem of fine tuning; although inflation neatly avoids many of the special initial conditions required by traditional big bang models, the ‘no-hair’ inflationary universe requires a few initial conditions of its own – namely a certain type of quantum field and a certain type of phase transition. Hence it can be argued that inflation has simply replaced one set of initial conditions with another.These are the technical drawbacks of the model of an inflationary universe. However, it is the philosophical implications of the theory that are most disturbing. Recall that inflation posits that a small region of space could have been inflated to our observable universe – this immediately raises the possibility that the universe we observe is just a fraction of a much larger, unobservable ensemble. Worse, one has to consider the possibility that other regions of space were inflated. As such regions would lie far beyond our horizon, they would effectively become parallel universes. This idea, that we live in one of a multitude of parallel universes (the multiverse) is not at all attractive to empirically minded physicists, but it has proved hard to rule out. Further, the theorist Andrei Linde has shown that it is unlikely that the inflation field was exactly the same everywhere; hence we can expect other universes to have different properties to our own (this theory is known as chaotic inflation.) Some claim that chaotic inflation offers an intriguing solution for the fine tuning problem – in a multitude of universes with vastly different properties , it is not so unlikely that at least one universe should have exactly the right conditions for life to emerge. However, most physicists dislike this sort of speculation. The problem was neatly summarized by the Archbishop of Canterbury a few years ago, when he stated “I find it disappointing that, in order to explain the properties of one observable universe, scientists are now postulating the existence of an infinite number of unobservable ones”! Touché.In conclusion, it is important to note that, far from being a contrived put-up job, the theory of inflation arose from fundamental considerations of particle physics14. Yet the theory provides a natural explanation for several aspects of our universe that are otherwise hard to explain – its homogeneity, its geometry and its large-scale structure. In particular, the theory predicts that the universe should exhibit a flat geometry. This prediction seemed in glaring conflict with observational data at the time, but that was soon to change…Chapter 7 Dark energy and the accelerating universeIn this chapter, we will see how modern measurements of the cosmic microwave background gave convincing support for both the big bang model and the theory of inflation. We shall also see how a new method of estimating astronomical distance led to the discovery of the accelerating universe. These data combine to form today’s model of a flat, accelerating universe that contains dark matter and dark energyThe discovery of the cosmic microwave background (CMB) heralded a new era in cosmology. However, the ensuing study of the background radiation led to several puzzles, which in turn led to the development of the theory of cosmic inflation (chapter 6). Inflation caused something of a divide between theorists and experimentalists; many theoreticians now believed in an inflationary universe of flat geometry1, while astronomers measured a universe with a low mass density and thus open geometry. Which was the real universe?A second disjunction of theory and experiment gradually emerged. It was realized from the first that the seeds of today’s galaxies and galaxy clusters should be detectable as small perturbations in the temperature of the cosmic background radiation. Yet non-uniformities in the radiation were not detected throughout the 1980s, despite the use of sensitive detectors on balloon flown high above the atmosphere2; the radiation appeared stubbornly smooth. The COBE mission In 1989, the Cosmic Background Explorer (COBE) was launched into orbit 900 km above the earth (figure 10). This was the world’s first satellite measurement of the cosmic microwave background radiation; the project had been planned since the 1970s, but had suffered a number of mishaps and delays.3The mission had two main aims; to measure the shape of the full spectrum of the background radiation and to search for minute fluctuations in the radiation. The spectrum was mapped by an instrument known as FIRAS while the fluctuations were measured by a Differential Microwave Radiometer (DMR)4. In 1990, the FIRAS results were announced; the measured spectrum of the background radiation fitted the theoretical spectrum of a black body most precisely (figure 11). This was a result of great significance as it constituted evidence that the radiation was of primeval origin, effectively ruling out many alternative models5. The data were presented at a meeting of the American Astronomical Society in 1990 and led to a standing ovation for John Mather, the instrument’s chief designer. Figure 10a; the COBE satellite at an altitude of 900 km above earthFigure 10b; spectrum of the CMB as measured by the FIRAS instrument aboard the COBE satellite. The data (squares) fit perfectly to the theoretical spectrum of a perfect blackbody (solid curve)In April 1992, the data from COBE’s DMR experiment were announced; small variations in the temperature of the radiation had at last been observed! However, the fluctuations were tiny indeed, of the order of one part in 100,000 or 0.001%. Small wonder that they had not been observed earlier.The COBE measurements provided a significant boost to the big bang model; the spectrum of the microwave background was exactly as predicted and perturbations in the radiation corresponding to the seeds of structure had finally been detected. Granted, these ripples were extremely small; it was hard to see how they would lead to today’s galaxies in the standard big bang model. However, the theory of inflation provided a ready answer, as we saw in chapter six. When George Smoot, chief scientist on the DMR instrument, presented the results at a press conference in 1992, he described the data as ‘direct evidence of the birth of the universe’ and said that looking at the data was ‘like seeing God if you are religious’. 6Soon afterwards, the famous cosmologist Stephen Hawking described the COBE results as ‘the most significant scientific finding of the twentieth century’. Some years later, John Mather and George Smoot were awarded the Nobel prize in physics “for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation”. The Hubble Space TelescopeAnother important advance was the launch of the famous Hubble Space Telescope (HST). The concept of an observatory orbiting in space had been mooted for many years, and after many delays the HST was finally launched aboard the space shuttle Discovery in 1990. After some initial problems, the telescope began taking breath-taking images of deep space from 1993 onwards7.These images have become icons of our age and led to a great upsurge of interest in astronomy (see figure 11). The new Space Telescope extended measurements of the cosmos by detecting Cepheid variables (see chapter 1) in galaxies much further way than ever before. The result was a more accurate estimate of Hubble’s constant (73 +/- 1 km/s/Mpc), settling the dispute between Sandage/de Vaucouleurs (see chapter 5). Ironically, the revised Hubble constant presented a new version of the age problem; it implied an age for the universe that was uncomfortably close to that calculated for some galaxy clusters!8Figure 11a; the Hubble space telescope Fgure 11b Iconic image of the ... galaxy taken by the Hubble space telescope The accelerating universeAn exciting new method of measuring the cosmos was discovered towards the end of the 1990s. This was the technique of using supernovae for the calibration of astronomical distance9. A supernova is what occurs when a certain type of star collapses to form a black hole; during this event, the material of the star is spewed outwards in a gigantic explosion that is extremely luminous. Supernovae are very rare events, but as ever more sophisticated telescopes reached further into space (and back in time) more of them were observed. More importantly, it was discovered that the luminosity of a particular type of supernova – type 1a - is extremely uniform, ideal for the calibration of the astronomical distance10. During the 1990s, two teams of astronomers sought to extend the Hubble graph using type 1a supernovae as distance markers; the Supernova Cosmology Project led by the American physicist Saul Perlmutter and the High-Z Supernova Research Team led by the astronomer Martin Schmidt. By 1998, both teams had reported an astonishing discovery; the most distant galaxies were dimmer (i.e. further way) than expected from simple extrapolations of the Hubble graph, by a factor of about 25%! This was a curious finding indeed. Although we refer continually to the ‘Hubble constant’, physicists had long expected to observe a decrease in the rate of the expansion of the universe at the largest distances, due to the gravitational pull of the galaxies. But the supernova measurements pointed to a rate of expansion that is increasing, a finding now known as the acceleration of the universe.Despite initial scepticism, painstaking observations of more supernovae suggested that the effect was real and that there was an unknown force of expansion at work in the cosmos. It seemed ordinary matter and dark matter did not comprise the total energy density of the universe; there was a contribution from an unknown source that became known as dark energy. 11 Dark energyThe discovery of dark energy marked yet another paradigm shift in cosmology. But what was the physical process responsible for the phenomenon? Several explanations were proposed, but the simplest was an old friend; perhaps the accelerated expansion was evidence of a cosmological constant. Recall that Einstein added a cosmological constant to the equations of relativity in order to predict a static universe, interpreting it as a constant energy of space that acts to counterbalance the inward force of gravity at the largest scales. With Hubble’s observation of the galaxy redshifts, Einstein dropped his cosmological constant, declaring it his ‘greatest blunder’ (see chapter 2). However, Lema?tre and others considered it an important component of relativistic models of the universe and used it to reconcile the age of the universe measured from the Hubble graph with the known age of stars. When Hubble’s estimates of astronomical distance were revised by Baade and Sandage in the 1950s, it seemed the cosmic constant could be safely set to zero. However, it never really disappeared from mathematical models of the universe and now it was back with a vengeance.Considering the new Hubble graph of figure 12, a quantitative estimate of the contribution of dark energy can be obtained by fitting a curve to the data. Recall that the density of matter in the universe is defined in terms of the parameter ?, the ratio of the actual density of matter to the critical value required to close the universe. This definition must now be extended to include a new term ?Λ , representing the contribution of dark energy. Thus, the geometry of the universe will be determined by the sum of two contributions i.e. ?total = ?M + ?Λ. (As before, ?total <1 denotes a universe of open geometry, ?total >1 denotes a universe of closed geometry and ?total =1 is the special case of a flat universe). It is clear from fig 12 that the astronomer’s favourite, an open universe of low matter density and no dark energy (?M = 0.3, ?Λ = 0) does not fit the data well, nor does a universe of flat geometry and no dark energy (?total = 1, ?Λ = 0). By far the best fit is obtained if one assumes a universe of flat geometry (?total = 1) with a dark energy contribution over twice that of matter. Taking the observational value of ?M = 0.3 for the matter density then suggests a value of about 0.7 for ?Λ. However, these estimates are provisional as the fit only provides an estimate of the relative contributions of dark energy and of matter; it does not provide an independent estimate of either, or indeed of the overall geometry of the universe12.Figure 12 Supernovae measurements show the Hubble graph is not linear at the largest distances. Three possible fits to the data are shown; the best fit is obtained with a model with ?M = 0.3 and ?Λ = 0.7 (top line). Data and fits from [12]In sum, the discovery of an accelerated expansion indicated a universe with two contributions to its energy density and thus to its geometry. One contribution, ?M, comes from both ordinary matter and cold dark matter. Another contribution, ??, acts to oppose the gravitational effect of matter and became known as dark energy. Fits to the data suggested a relative contribution of about 30% from matter and 70% from dark energy respectively; from the known density of matter this in turn suggests a universe of flat geometry, in pleasing agreement with the predictions of inflation. However, further measurements were needed in order to obtain independent estimates of each contribution and of the overall geometry of the universe. Could the observed acceleration be some type of systematic error in the supernova data? This possibility was ruled out when measurements of even more distant (and older) supernovae showed evidence of a de-accelerated expansion13. It seems dark energy became significant only when the universe reached a certain age; after a gradual slowing for the first seven billion years or so, the expansion then began to speed up! More recent studies of a great many supernovae have confirmed the current acceleration beyond doubt14. It should also be noted that the concept of dark energy did not come as a complete surprise to many theorists. In the first instance, inflation predicted a universe of flat geometry; given the observational value of ? = 0.3 for the density of matter, this pointed to another density contribution of unknown origin. Secondly, there was the age problem; some theoreticians had already resurrected the cosmological constant in order to ease the tension between the calculated age of globular clusters and the revised value of the Hubble constant15. It is impressive that many papers were written on this subject before the supernova data were announced; the latter must have been a pleasant surprise for those authors16!Dark energy and the cosmic microwave backgroundMeanwhile, measurements of the cosmic background radiation continued. It was soon realised that accurate measurements of the fluctuations in the background radiation could also reveal the presence of dark energy. This is because the angular scale of the perturbations indicate whether the geometry of the universe is open, closed or flat - and thus reveal a contribution from dark energy17. The COBE satellite had already detected ripples in the CMB, but more accurate measurements were needed in order to determine their scale.In 1999, two balloon experiments reported new measurements of fluctuations in the cosmic microwave background. (Such experiments are significantly cheaper than satellite missions, but only a small part of the sky can be mapped). The BOOMERANG project took data at an altitude of 42 kilometres above the Antarctic for a period of ten days, while the MAXIMA project was launched from Texas. The results suggested a value of ?total = 1.00+/- 0.05, i.e. the geometry of the universe is indeed flat to within an experimental error of less than 5%! This was an important advance; taking the observational value of ?M = 0.3 for the density of matter, it suggested a dark energy contribution of 0.7, in good agreement with the supernova results18. It is always a good moment in science when different lines of enquiry point towards the same result and the next experiment was to prove even more satisfying…Fig 15. The BOOMERANG experiment gave the first direct experimental measurement of the geometry of the universeThe WMAP missionIn 2001, the Wilkinson Microwave Anisotropy Probe (WMAP) was launched into orbit. This experiment comprised highly sensitive instruments on board a satellite 1.5 million kilometres from earth, calibrated to measure fine variations in the entire spectrum of the microwave background. The measured variations are plotted as a function of angle in figure 13, a plot known as the angular power spectrum (the temperature is expressed in multipoles and the intensity is plotted as a function of multipole number, a representation that arises from a mathematical co-ordinate system known as spherical harmonics). The dominant feature of the spectrum is the large peak on the left hand side, known as the ‘first acoustic peak’. Theory predicts that this feature is a direct measure of the curvature of space and the WMAP data implies a value of ?total = 1.0 +/- 0.02, in excellent agreement with the balloon experiments. The spectrum also gives an estimate of ?M = 0.27 for the contribution of the matter density alone, in good agreement with astrophysical observation. Combined together, these results suggest a value of ?Λ = 0.73 for the contribution of dark energy, in excellent agreement with the supernova results.A theoretical fit (solid line) to the data is also shown in figure 13. This fit has been computed with the use of the parameters ?total = 1.0, ?Λ = 0.73 and ?M = 0.27 19. It can be seen from the diagram that these parameters give a very good fit indeed to the data. By contrast, none of the main alternative models (a flat universe with no dark energy, a curved universe with no dark energy or a curved universe with dark energy) give a good fit, as can be seen in figure 14. By far the best fit is obtained by assuming a model of a flat universe containing ordinary matter, cold dark matter, and dark energy. Fig 13 Anisotropies of the CMB as a function of angle, known as the power spectrum. The solid line is that predicted by the Λ-CDM model with the parameters ?total = 1.0, ?Λ = 0.73 and ?M = 0.27Fig 14 Alternative fits to the power spectrum. The solid line is that predicted by the Λ-CDM model with the parameters ?total = 1.0, ?Λ = 0.73 and ?M = 0.27The Λ-CDM modelThe experiments of this chapter - the COBE satellite mission, the supernova measurements, the BOOMERANG and MAXIMA balloon experiments and the WMAP mission – led inexorably to a new version of the big bang model. This view is now known as the standard or Λ-CDM model and it states that we live in an accelerating universe of flat geometry that contains ordinary matter, cold dark matter (CDM) and dark energy. The Λ symbol indicates that the dark energy is associated with a non-zero cosmological constant that is thought to arise from a natural tendency of space to expand, opposing the gravitational effect of matter. Note that the moniker is slightly misleading as we expect three contributions to the mass/energy density of the universe; these contributions are estimated as 74%, 22% and 4% for dark energy, dark matter and ordinary matter respectively (see figure 15). Figure 15 Pie chart of the relative contributions of dark energy, dark matter and ordinary matter to the mass/energy density of the universeNote also that the observation of flat geometry fits very nicely with the hypothesis of inflation; as we have seen, it is quite difficult to explain why the observable universe should exhibit this geometry without some form of inflation in the first fractions of a second. We also saw in chapter 6 that inflation predicts fluctuations in the cosmic microwave background of the right order of magnitude. Indeed, the theory predicts that the spectrum of fluctuations will have a shape that is very nearly independent of scale (characterized by a spectral index ns that is close, but not exactly equal to 1.0 to an accuracy of 10%). It is exciting to note the spectrum in figure 13 has exactly such a shape; the fit has been computed by taking a spectral index of ns = 0.95 +- 0.0219.Finally, we note that, for all the exciting successes of this chapter, the term Λ-CDM also highlights the shortcomings of the model; we do not know what physical substance makes up either dark matter or dark energy and hence it could be argued that we do not know what 96% of the universe is made of! This puzzle will be discussed further in the next chapter, along with other outstanding problems.Chapter 8 Putting it all togetherIn this chapter, we review the modern version of the big bang theory, the Λ-CDM model. We review the outstanding puzzles of inflation, dark energy and the singularity and finally address the key question: is it true?In the first part of this book, we encountered the four main planks of evidence for the big bang model; the recession of the galaxies (Hubble’s law), the abundance of the lightest elements, the distribution of the radio galaxies and the cosmic microwave background. In the second part, we saw that advances in astronomy and detailed study of the background radiation led a new version of the model, a theory that suggests we live in an expanding universe of flat geometry that contains dark energy, dark matter and ordinary matter.Put together, a picture emerges of a universe that originated in an incredibly hot, dense state with energy in the form of radiation and elementary particles. The universe expanded and cooled, with nuclei of the lightest elements forming after one second and atoms forming after about 100,000 years. The latter process rendered the universe transparent to radiation, allowing it to travel unimpeded for the first time; this radiation is observable today as the cosmic microwave background. Evidence of the seeds of today’s galaxies are detectable as small variations in this background radiation, and calculations suggest that natural fluctuations in density of the infant universe could have given rise to these variations if an inflationary phase of the universe occurred in the first fraction of an instant. This view is summarized in figure 16. Quantitative parameters of the model can be extracted from the experimental data of chapter 7. This data has been backed by several recent experiments, notably the SLOAN Sky survey and the PLANCK satellite. The best fit is a universe that is 13.7?±?0.1 billion years old and has a current expansion rate of 70.4?±?1.4?km/s?1/Mpc . It is geometrically flat to an accuracy of 0.2 %, with an energy density made up of 4.56 ?±? 0.16% of ordinary matter, 22.7 ?±? 1.4% of cold dark matter and 72.8?±? 1.6% of dark energy; the latter leads to a slight acceleration in the current expansion. Density fluctuations observable in the cosmic background radiation are well modeled by a spectral index of ns = (0.963 +/- 0.012) predicted by the theory of inflation. Outstanding puzzlesThe CDM big bang model fits the data exquisitely well and it is also self-consistent. Evidence from different lines of enquiry all point to the same model, from the relative abundance of the chemical elements to the masses of stars, from supernova measurements of the accelerated expansion to estimates of the geometry of the universe from measurements of the microwave background. However, the model also features several outstanding puzzles. To a physicist, the situation is rather like a jigsaw puzzle that is missing several crucial pieces; we have an idea what the overall image will look like, but major gaps remain (and the completed puzzle may one day turn out to be part of a much larger ensemble). The most outstanding of these gaps are the nature of dark matter, the nature of dark energy, the nature of the inflationary field and the nature of the singularity itself. The puzzle of dark matterWe recall from chapter 6 that the concept of dark matter was first mooted by Fritz Zwicky in the 1930s in order to explain the rotational motion of certain galaxies. Since that time, the hypothesis of dark matter has been invoked by astronomers to explain the behaviour of matter at almost all astronomical scales, from the motion of stars to that of galaxies, from galaxy clusters to galaxy halos. Additional evidence comes from gravitational lensing, a phenomenon whereby multiple images of a light source are seen due to the bending of light by unseen matter between the source and observer1. Essentially, the astronomical hypothesis is that dark matter is an entity that neither emits nor scatters light or other electromagnetic radiation (and so cannot be directly detected via optical or radio astronomy), but is observable by its gravitational effect on ordinary matter2. In the last chapter, we have seen that there is an additional cosmological basis for the hypothesis of dark matter; measurements of inhomogeneites in the cosmic microwave background suggest that about 22% of the total energy density of the universe is in the form of matter that is not strongly interacting. Hence, astronomy and cosmology provide indirect evidence for the existence of dark matter - but is there any direct evidence? An exciting breakthrough occurred in 2006, when astronomers measured a merging of two galaxies into a single cluster, now known as the bullet cluster. This dramatic effect was observed by the CHANDRA X-ray satellite observatory, launched by NASA in 1999. Each galaxy appeared to comprise two separate components that behaved very differently during the collision. The stars of each galaxy were not greatly affected and passed more or less straight through, if slowed slightly due to gravitational effects. (Gases in each galaxy slowed more due to their electromagnetic interaction). Most importantly, a large component of matter in each galaxy (detected before and after by the gravitational lensing of background objects) showed no interaction whatsoever – which is exactly what one would expect of dark matter. This was exciting news indeed and similar effects have since been observed in other galaxy collisions3. However, while such observations give strong evidence for the existence of dark matter, they tell us little about the nature of the phenomenon.Figure 15: In the merging of two galaxies into the bullet cluster, each galaxy is seen to comprise an interacting and non-interacting component Cosmologists have expected for many years that experiments in particle physics should throw up candidates for dark matter. Obviously, certain constraints apply; it must be weakly interacting matter (because it is not seen by telescopes at any wavelength) and there must be enough of it to account for 22% of the energy density of the universe. We also saw in chapter 7 that it must be cold, i.e. travel at non-relativistic speeds. The leading candidate for such matter is known by the acronym WIMPs, i.e. weakly interacting massive particles. However, the identity of such particles has remained elusive. There are currently many experiments underway to detect possible candidate particles for dark matter. These experiments are very difficult technically as WIMPs are expected to interact extremely weakly with any detector. Hence, the experimenters must measure huge numbers of interactions in the hope of finding a few rare WIMP events. The experiments take place in large underground laboratories in order to shield the apparatus from incoming cosmic rays. Examples include the CDMS experiment in the Soudan mine in Minnesota (US), the SNOLAB underground laboratory at Sudbury in Canada, the DAMA/LIBRA experiment at the Gran Sasso National Laboratory in Italy, the Boulby Underground Laboratory in the UK and the Deep Underground Science and Engineering Laboratory in South Dakota (US).Most of these experiments employ detectors at extremely low temperatures that measure the heat produced when a particle hits an atom in crystalline absorbing material, although some use liquid detectors to detect collisions of dark matter particles with liquid molecules. One group, the DAMA/LIBRA experiment at Gran Sasso, have detected an annual effect that they suspect is due to dark matter. However, this claim is controversial as it has not been reproduced in other experiments4. At the time of writing, the CDMS experiments such as the CDMS (above) and the XENON 100 experiment at Gran Sasso are thought to provide the most sensitive limits on WIMP detection; so far, their data have shown null results 5.The puzzle of dark energyWe have seen that the concept of dark energy was raised by the supernova measurements of the accelerated expansion in1998 1. Since then, further supernova studies and WMAP measurements of perturbations in the CMB have added weight to the hypothesis, fixing the dark energy contribution at about 73% of the total energy density of the universe. Dark energy is not incompatible with the theory of inflation (it fits well with inflation’s prediction of a universe of flat geometry) but the two concepts should not be confused – the former concerns a slight acceleration in the expansion of the present universe over millions of years, while the latter concerns an enormous, exponential expansion in the infant universe that lasted only a fraction of a second. The simplest explanation for dark energy is the hypothesis of a cosmological constant, first mooted by Einstein and later retained by Lema?tre. Mathematically speaking, such a factor arises naturally within the framework of general relativity; as a constant of integration, the constant can be of any value and there is no particular reason why it should be zero2 . In terms of a physical interpretation, we can follow Einstein by ascribing the constant to a natural tendency of space to expand. This hypothesis concurs nicely with a prediction from modern quantum physics: that particles and anti-particles can pop in and out of existence in the vacuum in accordance with Heisenberg Uncertainty Principle, leading to a repulsive energy that we measure as the cosmic constant. However, there are two major problems with this simple model of dark energy. In the first instance, quantum calculations suggest that if such a vacuum energy exists, it should be many orders of magnitude larger than our measurements of dark energy (by a factor of about 10150 in fact). This is quite a mismatch of theory and experiment and is known as the vacuum catastrophe. It is of course possible that there is some as-yet unknown symmetry mechanism that causes the various contributions to vacuum energy to cancel; however, it seem unlikely that such a mechanism could lead to a value that is extremely close to zero, but not equal to it.A second puzzle is the size of dark energy relative to dark matter; although the contribution of dark energy to the total energy density is about twice as large as that of matter, the two contributions are within an order of magnitude. But if dark energy is a cosmological constant, it remains constant while the density of matter decreases over billions of years in an expanding universe. Again, it seems something of a coincidence that the two contributions should be the same sort of size in our own particular epoch..In consequence, several alternative explanations for dark energy have been proposed. Possibly the best-known alternative is the notion of quintessence. Quintessence is a hypothetical form of dark energy that differs from the cosmological constant in that it is dynamic i.e. can change over time. Furthermore, it is hypothesised that quintessence can be either attractive or repulsive depending on the ratio of kinetic to potential energy in the universe. In this model of dark energy, it is thought that a repulsive quintessence may have been triggered once a balance between radiation and matter was established in the early universe. The phenomenon may have been of negligible size at that epoch, but eventually grew to dominate the universe today. Note that quintessence offers an explanation for dark energy that is outside the context of general relativity, while the cosmological constant arises naturally within the framework of the general theory.To decide between a cosmological constant or quintessence as models for dark energy is straightforward in principle, as the former is constant over time while the latter varies. Hence a new generation of sophisticated experiments will attempt to measure the evolution of dark energy over time, by measuring the expansion rate of the universe at earlier and earlier epochs with the use of the most distant supernova of all20. Finally, we note an interesting connection between dark energy and inflation; the observation of an accelerated expansion in the current epoch does in principle support the idea of different expansion rates at different epochs. Some cosmologists go much further than this, speculating that the current acceleration of the universe may in fact be a faint echo of inflation – a leftover from the exponential expansion of the infant universe. However, the recent discovery that the expansion was de-accelerating in the epoch before the current acceleration casts doubt on this hypothesis3.The puzzle of inflationWe have seen in chapter six how the postulate of an inflationary phase in the infant universe offers a neat solution to the horizon and flatness problems. In addition, it provides a mechanism for the formation of galaxy structure and may even shed some light on the singularity problem. We have also seen that the theory is supported by modern measurements, from precision measurements of the cosmic microwave background to the detection of the acceleration of the expansion.However, while the general idea of inflation has become part of the standard model of cosmology, the specific nature of the inflationary field remains an outstanding problem. It was originally proposed that inflation was driven by a Higgs –like quantum field; it later emerged that such a field will not do. In recent years, a great many alternate models of inflation have been proposed; however, there has been no success to date in uniquely identifying a successful model. It is hard to see how inflationary cosmology can make concrete progress until we know more about the nature of the field. From the point of view of experiment, it is a matter of some concern that no hint of the existence of a quantum field with the necessary characteristics has ever been observed in the world of particle physics. In sum, one could argue that it is unfortunate that the whole edifice of the big bang rests on a quantum field that has never been detected.In addition to this puzzle, one has the philosophical problems associated with inflation. As we saw in chapter six, the theory seems to lead inevitably to the hypothesis of chaotic inflation and the multiverse. Many physicists are concerned by the extravagant scenario of the multiverse and uncomfortable with the notion of the existence of worlds that can never be measured in principle. Of course, these possibilities may one day be ruled out, but for the moment, they are an unattractive feature of the theory of inflation.The problem of the singularityWithout doubt, the greatest challenge of all is the big bang itself. We have noted before that the name ‘big bang’ is a misnomer as the model tells us nothing about the bang itself. The general theory of relativity provides a successful framework for a description of the evolution the universe from the first fractions of a second to the current epoch, but not of its origin. Indeed, at first sight, relativity implies a universe that begins in a singularity , i.e., in a point of zero volume, infinite density and infinite temperature (see figure 4). Physicists do not take this prediction literally because mathematical singularities are not usually a reliable description of the physical world; more importantly, we do not expect general relativity to give a reliable description of the micro-world. We have strong evidence the universe was once smaller than an atom, but phenomena on the atomic scale are described by the strange laws of quantum physics, a micro-world in which the rules are very different from those of ordinary physics. Hence, a successful analysis of the bang will necessitate an understanding of the behavior of gravity on quantum scales. Such a theory - a quantum theory of gravity - has not so far been forthcoming. This problem is the reason one talks about a ‘big bang model’ rather than a ‘big bang theory’; the model is clearly incomplete. To describe the behaviour of gravity on quantum scales will require a synthesis of the two great pillars of modern physics, general relativity and quantum physics. This is a major topic of research and has led to a convergence of two very different fields, cosmology (the study of the universe on the largest scales) and particle physics (the study of the world of the sub-atomic). Some progress has been made, particularly in the context of string theory; in this theory, the elementary particles are described as excitations of minute strings. More recently, this idea has been broadened to M- theory, where the strings are replaced by two-dimensional membranes.An intriguing aspect of the theory of inflation is that may speak to the problem of the singularity. This idea arises from a consideration of the Heisenberg Uncertainy Principle , a fundamental tenet of quantum physics. According to the uncertainty principle, the tiniest particles of matter can in principle appear out of the vacuum if they disappear again quickly enough. It seems they can borrow energy to exist, as long as that existence is extremely short. (The concept arises from a fundamental indeterminacy in quantum entities)20. This phenomenon has long been known and evidence of the existence of such virtual particles and anti-particles is routinely detected indirectly in accelerator experiments19. Now inflation is hypothesised to occur to a tiny patch of space over a timespan of fractions of a second; hence one expects quantum processes to be relevant. This raises an intriguing possibility: if virtual particles briefly appear in a minute region of space and that region undergoes inflation, could they be blown up to become our entire universe? This scenario may seem rather speculative but it is taken seriously by many theorists because it offers the first glimpse of a possible explanation for the hardest question of all – how does something arise from nothing? The concept of a universe ex nihio became extremely well-known when it was popularized by the cosmologist Stephen Hawking22. We shall return to this question in the epilogue.The cyclic universeOne intriguing idea that has emerged from the string theory approach to cosmology is the possibility of multiple bangs, i.e., the cyclic universe. In this scenario, the Universe undergoes an endless sequence of cycles in which it contracts in a big crunch and re-emerges in an expanding big bang. Hence the big bang is not the beginning of time; rather, it is a bridge from a pre-existing era. This theory, the cyclic universe, has recently been expounded by the veteran cosmologists Paul Steinhardt and Neil Turok. In the cycle universe, each cycle proceeds through a period of radiation and matter-domination consistent with standard cosmology, producing the observed abundance of elements, the cosmic microwave background and the recession of the galaxies. For the next trillion years or more, the Universe then undergoes a period of slow cosmic acceleration that ultimately empties the Universe and triggers the events that lead to contraction and a big crunch. The transition from big crunch to big bang automatically replenishes the Universe by creating new matter and radiation. What is the proposed mechanism for this process? In the cyclic model, the Universe consists of two branes (surfaces) bounding an extra dimension and the big bang corresponds to a collision of the two branes. Each bang is a transition from big crunch to big bang due to the collapse, bounce and re-expansion of the extra dimension. Instead of the collapse of all dimensions to a singularity predicted by relativity, the cyclic model suggests that one higher dimension shrinks; our usual space dimensions remain infinite and time runs continuously. At first sight, one might argue that the cyclic model simply complicates an old problem by replacing one big bang with a multitude. However, the point is that the model sidesteps the problem of the singularity because there is no longer any need to postulate an explosive beginning to space and time. Instead, space and time may have always existed in an endless cycle of expansion and rebirth. In addition, the temperature and density of the universe do not become infinite at any point in the cycle.One intriguing aspect of the model is that it offers an alternative to inflation. In the cyclic universe, the flatness and homogeneity of the universe are not set by a hyper-expansion in the initial moments, but by conditions existing before the bang. Similarly, the seeds for galaxy formation were created by instabilities arising as the Universe was collapsing towards a big crunch prior to our big bang. Best of all, the phenomenon of dark energy is crucial to the model, rather than an unexpected add-on; it is dark energy that drives the universe to the end of each cycle once matter has formed.It is important to note that the cyclic universe does not replace the Big Bang model; instead, it postulates that the big bang is part of a grander scheme. In addition, it offers an intriguing solution to certain troublesome aspects of the Big Bang model ( the nature of inflation, dark energy and the singularity). Some physicists are quite excited about the cyclic model while most are cautious or sceptical. Certainly, it is interesting that the model recoups all of the successful predictions of the big bang/inflationary theory, while addressing several questions that the big bang/inflationary model does not address. However, the mechanism of the cyclic model relies heavily on ideas in modern string theory that remain untested. For this reason, it will probably remain a speculative idea for most physicists for many years. Indeed, one of the great challenges of modern physics is how fundamental ideas in string theory may be tested experimentally.The above are all respectable theories; however, it should be borne in mind that they are highly speculative. So far, there is no evidence that more than one bang occurred in our universe , while there is a great deal of evidence that at least one bang did occur.2 Most physicists (including this one) take the view that slowly constructing an accurate picture of the bang we know about is enough to be going on with for now….NotesChapter 51 This is something of a simplification as it assumes the cosmological constant is zero2 The astronomer Alan Sandage wrote a famous paper titled ‘ Cosmology – the search for just two numbers’, indicative of this approach to observational cosmology3 There is a great description of this work in the book ‘The Cosmological Distance Ladder’ (Rowan-Robinson , 1985)4 Sandage estimated a value of 50 kilometers per second per megaparsec (km/s/Mpc) while de Vaucouleurs got a value of versus 90 km/s/Mpc; the Hubble Space Telescope (HST) provided a final answer of 70 km/s/Mpc. This story is very well told in the book ‘Lonely hearts of the cosmos’, by Dennis Overbye5 In other words ? = ρ/ρc, where ρ is the actual density of matter (a variable) and ρc is the critical density (a constant). The critical density is related to the Hubble constant by the equation ρc = 3 H02/8ΠG where G is the gravitational constant6 For example, the mass of our sun can be estimated from measurements of the earth’s orbit7 There is no law that dictates that all matter be visible i.e. interact with the electromagnetic force. It should be noted that the one alternative is that our laws of gravity are wrong, a theory known as Modified Newtonian Dynamics or MOND. However, this theory has lost support in recent years as modern observations support the existence of dark matter at every scale (see Rowan-Robinson , 1985).8 The nature of particles that make up dark matter is a vibrant field of study today. A good review can be found in .........9 There is a good description of this method in ‘The Cosmic Century’ (Longair, 2006) 10 IbidChapter 6This observation is usually attributed to the data from satellite measurements; in fact the homogeneity of the universe was observed empirically long before thisThe problem was first pointed out by Robert Dicke (Dicke, 1970). The calculations show that this scenario results if ? differs from unity by a factor of even 1 in10-15?when the universe is 1 nanosecond oldAn exponential growth is extremely fast; it is written as en where e =2.718 and n can be any number. In Guth’s proposal, the universe is proposed to have grown by a factor of about 1050 during a timespan of about 10 -30 sA very good history of the development of the theory can be found in Kolb and Turner (1994)Guth’s first major paper on the subject was specifically titled Inflationary Universe; A Possible Solution to the Horizon and Flatness problems (Guth 1981)This is the key point: the starting point is vanishingly small (about 10-28 m)In analogy with Hawking’s no-hair theorem for black holesQantum tunneling is the process whereby quantum particles penetrate a barrier that should be too high for them to cross, according to classical physicsLinde had independently developed his own model of inflation, so he was quick to appreciate the problem. As a tongue-in-cheek tribute to Guth he titled his paper A New Inflationary Universe Scenario; A Possible Solution of the Horizon, Flatness, Isotropy, and Primordial Monopole Problems (Linde, 1982)Technically speaking, new inflation posits a second-order phase transition, rather than the first-order phase transition of the Guth model. There is an excellent description of the difference between new and old inflation in chapters 11 and 12 of Guth’s book (Guth, 1997)The fuzziness is specified by the Heisenberg Uncertainty Principle, a theorem that predicts a fundamental ambiguity in the properties of quantum entities. For example, a particle cannot possess an exact position and momentum simultaneously; the more definite its position, the less defined its momentum. (It is not a problem of measurement, as is often stated).The occasion was the 1982 Nuffield Workshop on Cosmology in Cambridge. There is a great description of the process of discovering this result in chapter 13 of Guth’s book (Guth 1997)This is a slight simplification; in fact the work showed that inflation could give rise to the shape of the CMB spectrum. The amplitude of the perturbations depended on the nature of the inflationary field which was not knownThe problem Guth was addressing is that Grand Unified Theories of particle physics predict the existence of magnetic monoples, none of which have ever been observed; an observable universe that is only a fraction a much larger universe could explain the low density of monopoles. It is noteworthy that his model is firmly grounded in ideas of particle physics, rather than cosmology.Chapter 7Given the low value of mass density from observation, some theorists wondered about an additional contribution to the energy density, as we shall seThere is a very nice overview of this period in Marcus Chown’s book (Chown 1997). Including the tragedy of the Challenger Disaster. There is a very good overview of the buildup to the COBE experiment in chapter 6 of the book ‘Wrinkles In Time’ (Smoot, 1997)The DMR instrument provided sensitive measurements of the background radiation from two different directions simultaneouslyFor example, a background of numerous stellar and gaseous emissions could not produce such a spectrumSmoot’s announcement of the results was quite controversial, as explained in the book ‘The Very First Light’ (Mather and Boslough, 1996) One of the telescope mirrors was found to be flawed and had to be replaced by astronauts It was later realised that this mismatch occurred because the calculation of the age of globular clusters assumed a matter-filled universe with no cosmological constantType 1a supernovae occur when a white dwarf star collapses to a black hole. The process leads to a luminous source that is extremely uniform and ideal for the calibration of astronomical distanceThe fascinating story of the discovery of the accelerating universe is told by one of the participants in the book ‘The Extravagant Universe’ (Kirshner 2002)It is not known who first coined the term dark energy, but it is probably named in analogy with dark matter. It is an unfortunate term as students often confuse the two, and the confusion is heightened when one recalls the mass-energy equivalence of relativityThe data and fitting of figure 12 is taken from Perlmutter’s 1999 publicationThis point is often overlooked. If the acceleration was a systematic error, it would affect all the supernova data. In fact, measurements of supernovae at the largest redshifts suggest a de-accelerated expansion; thus the universe underwent a change from a slowing expansion to an accelerated one See SLOAN surveySee note 8See for example Carroll, Press and Turner (1992), Krauss and Turner (1995) or Krauss (1998)A measurement of the angle covered by an object of known size at a known distance gives information about the surrounding geometry. The maximum size of fluctuations in the CMB is 300,000 light years (because recombination occurs at 300,000 years) and they are viewed at a distance of about 14 billion light years; hence a measurement of the angle gives an estimate of the geometry of the universe Actually, one doesn’t need to assume a value for ?M. Since the balloon measurements give an estimate of the sum ?M + ?Λ, and the supernova measurements give an estimate of the difference ?Λ - ?M, the two equations combined give independent estimates of each.Figures 13 and 14 are provided by David Kaiser of MIT. There is a very nice overview of fitting the predictions of inflation to this data in (Guth and Kaiser 2005)Chapter 8Gravitational lensing of distant objects by observable matter (massive stars) is a well-established phenomenon; thus multiple images of a distant source can be used to infer the presence of dark matter between source and observerA very good overview of the astronomical evidence for dark matter can be found in Rowan-Robinson’s bookIn essence, each galaxy behaves as a couple consisting of an aloof person and his friendly partner entering a party; they are soon separated as the ordinary matter stops to say hello, while the dark matter keeps right on going.See - for a good overview of the serach for the particles that make up dark matterA good overview of this controversy can be found in.....See . and .A good overview of each experiment can be found on their webpages. Paper on de-accelerationThere is a good discussion of the concept of quintessence in Steinhardt et all (1999)Einstein himself often warned of the dangers of extrapolating the laws of general relativity to atomic dimensionsOne of the great problems of modern science journalism is that there is often very little distinction between theories that are supported by a great deal of evidence, and theories that are notBibliography Alpher RA, Bethe H and Gamow G (1948) ‘The origin of the chemical elements’, Phys Rev 73 (7)Alpher RA, Follin JW and Herman RC, Phys Rev (1953) Phys Rev 92, 1347Alpher RA and Herman RC (1948) Nature 162Bertotti B., Balbinot R., Bergia S. and Messina A. (1990) Modern Cosmology in Retrospect CUP Carroll, Press and Turner (1992) Annual Rev Astronomy 30, p499Chown, M ( 1993) The afterglow of creation: from the fireball to the discovery of cosmic ripples (Arrow Books)Dicke, R. H. (1970). Gravitation and the Universe. American Philosophical Society.Einstein,A (1905) On the electrodynamics of moving bodies Originally published in German in Annalen der Physik 17 (10) 1905. See for a translation on the web.Einstein,A (1916) The foundation of the general theory of relativity, Annalen der Physik vol 354 (7) p769Einstein,A (1917) Cosmological considerations of the general theory of relativity Sitzungsberichte der K?nigliche Preussische Akademie der Wissenschaften (Berlin) 142-52Everitt,C.W.F. et al. (2011) "Gravity Probe B: Final Results of a Space Experiment to Test General Relativity".. Physical Review Letters. May, 2011Farrell J (2005) ‘The Day Without Yesterday; Lema?tre, Einstein and the birth of modern cosmology’ Thunder’s Mouth Press, NY 2005Friedman, A (1922) On the curvature of space, Zeitschrift für Physik vol 10, p337Friedman, A (1924) On the possibility of a universe with constant negative curvature of space, Zeitschrift für Physik vol 21, p326Galileo G (1610) Sidereus Nuncius (Baglioni)Guth A, (1981) Inflationary Universe; A Possible Solution to the Horizon and Flatness Problems Phys Rev D 23 (2)Guth A (1997) The inflationary universe; a quest for a new theory of cosmic origins (Jonathan Cape)Guth A and Kaiser D (2005) Science, vol 307 p 884Harrison, E (2001) Cosmology (Cambridge University Press)Hawking, SW, Penrose, R (1970) "The Singularities of Gravitational Collapse and Cosmology". Proceedings of the Royal Society A 314 (1519)Hawking SW (1988) ‘A Brief History of Time; From the Big Bang to Black Holes’ Bantam BooksHubble, Edwin (1929) A relation between distance and radial velocity among extra-galactic nebulae PNAS vol 15, 3 1929Hubble, Edwin and Humason ML (1931) The velocity-distance relation among extra-galactic nebulae APJ vol 74, p43Kragh, H (1996) ‘Cosmology and Controversy; the historical development of two theories of the universe’, Princeton University PressKennefick, D(2009), "Testing relativity from the 1919 eclipse- a question of bias," Physics Today, March 2009, pp. 37–42.Kirshner, R 2002 ‘The Extravagant Universe; Exploding stars, dark energy and the accelerating cosmos’ (Princeton University press)Kolb E and Turner M (1994) The Early Universe (Westview Press)Krauss L and Turner M (1995) Gen.Rel.Grav. 27 p 1137Krauss L (1998) Astrophysical Journal 501, p461Kuhn, Thomas (1976) The Structure of Scientific Revolutions (Harvard University Press)Latour, Bruno and Woolgar, Steve (1976) Laboratory Life; The Construction of Scientific Facts (Princeton University Press)Lema?tre, G (1927) A homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of extra-galactic nebulae, Annales de la societe Scientifique de Bruxelles, vol A47 p 29. Translated and reprinted as ‘The Expanding Universe’ in Monthly Notices of the Royal Astronomical Society vol 91 (1931) p 490Lema?tre, G (1931,a) ‘The beginning of the world from the point of view of quantum theory’ Nature, March 21, p 44Lema?tre, G (1931,b) ‘L’expansion de l’espace’, Revue Questions Scientifiques 17, p391McMullan Ernan (2005) ‘Galileo and the Church’(Univ Notre Dame Press)Linde A (1982) A New Inflationary Universe Scenario; A Possible Solution of the Horizon, Flatness, Isotropy, and Primordial Monopole Problems Physics Letters B, Volume 108, Issue 6Longair, M (2006) The Cosmic Century: A History of Astrophysics and Cosmology (CUP)Mather JC and Boslough J(1996) The Very First Light’ (Penguin) Overbye, D (1999) Lonely Hearts of the Cosmos: The Story of the Scientific Quest for the Secret of the Universe , Back Bay BooksPeebles (1972) Physical Cosmology (Princeton University Press)Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University PressPerlmutter S, Aldering G, Goldhaber G et al (1999) Measurements of omega and lambda from 42 high-redshift supernovae Astronomical Journal vol 517 (2) p 56Sandage, A (1970) ‘Cosmology: A search for two numbers’ Physics Today, February 1970 Smith, RW (1982) The Expanding Universe; Astronomy’s Great Debate (Cambridge University Press)Smoot G(1994) Wrinkles in Time (Harper Perennial)Weinberg, S (1993) ‘The first three minutes; a modern view of the origin of the universe’ (Basic Books)Zlatev, I.; Wang, L.; Steinhardt, P. (1999). "Quintessence, Cosmic Coincidence, and the Cosmological Constant". Physical Review Letters 82 (5): 896–899. Or arXiv: astro-ph/9807002 ................
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