Extending classical big bang theory

Chapter 21 Extending classical big bang theory The big bang is our standard model for the origin of the Universe and has been for almost half a century. This place in well earned. At a broader conceptual level, all of modern cosmology rests on observations (for example, the very existence of the cosmic microwave background radiation) that make sense only if there was a big bang or something very much like it in our past. At a more nuts and bolts level, the standard big bang model accounts quantitatively for a variety of relatively precise observational data (for example, those associated with specific properties of the cosmic microwave background and with the observed abundances of light elements) that would be difficult to explain with any competing theory. However, there are some observations in modern cosmology suggesting that the classical big bang is an essentially correct but perhaps incomplete picture of the origin and evolution of our Universe. In this chapter we address some of these issues. 841

842 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.1 Successes of the Big Bang Let us begin by being more explicit about the successes of the standard big bang and its place in the modern picture of cosmology. As we have already discussed to some degree in Chapter 16, The standard cosmology rests on a relatively few observations and concepts: 1. The redshifts of distant galaxies imply that we live in an expanding Universe described at the simplest level by the Hubble law. 2. On large enough scales (beyond that of superclusters of galaxies) the Universe appears to be both homogeneous and isotropic (cosmological principle). 3. The properties of distant quasars suggest that these powerful energy sources were once more energetic and more closely spaced than they are today, implying that the properties of the Universe on large scales has evolved with time. 4. The cosmic microwave background (CMB) is all pervading, highly isotropic but with measureable fluctuations at the one part in 10 5 level, and possesses an almost perfect blackbody spectrum with a temperature of 2.725 ± 0.001 K. 5. The elemental composition of the Universe is (by mass) three parts H to one part He, with but a trace of heavier elements.

21.1. SUCCESSES OF THE BIG BANG 843 6. Because gravitation and not electromagnetism governs the largescale structure of the Universe, it must be charge neutral on large scales. Conversely, observations indicate that the Universe is highly asymmetric with respect to matter and antimatter, with no evidence for significant equilibrium concentrations of antimatter. 7. There are many fewer baryons in the Universe than there are microwave photons. 8. In contrast to the homogeneity of the Universe on very large scales (cosmological principle), matter on scales comparable to superclusters of galaxies and smaller exhibits complex and highly evolved structure, This contrasts sharply with the smoothness of the CMB. Furthermore, observations indicate that this structure began to develop very early in the history of the Universe. 9. Detailed analysis of fluctuations in the CMB and of the brightness of distant Type Ia supernovae indicate that (a) The expansion of the Universe is presently accelerating. (b) The geometry of the Universe is remarkably flat (euclidean). 10. The bulk of the matter in the Universe is not luminous (dark matter), being observable only through its gravitational influence. 11. Various observational constraints imply that most of this dark matter is not baryonic.

844 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY The first five observations fit well within classical big bang cosmologies: Observations (1) (2) indicate that we live in an expanding, isotropic universe, Observations (3) (5) indicate that this Universe has evolved over time and had a beginning in a very hot, very dense initial state (the big bang). The remaining observations need not be inconsistent with the classical big bang, but they require either ad hoc imposition of particular initial conditions on the Universe, or assumption of specific properties for the microscopic properties of the matter and energy fields that the Universe contains that we shall address in the next section.

21.2. PROBLEMS WITH THE BIG BANG 845 21.2 Problems with the Big Bang As we have indicated in the previous section, observational properties (6) (11) constitute problems for the classical big bang model. They do not necessarily invalidate the big bang, but they indicate that the big bang in its minimal form may be incomplete. In most cases we shall find that this incompleteness is likely to originate in an inadequate understanding of how the particle and field content of the Universe couples to its evolution. Let us now discuss these problems.

846 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.2.1 The Horizon Problem Observational property (4) [isotopy of the CMB] presents a potential conflict with causality because The nearly constant temperature of the CMB in widely separated parts of the sky is understandable only if those regions were in causal contact in the past. But in the standard big bang it is easy to show that regions on the sky separated by more than a degree or two in angle could never have been in causal contact (had sufficient time to exchange light signals) since the big bang. That is, they lie outside each other s horizons, as illustrated in Fig. 21.1 on the following page, and thus cannot have been in causal contact in the past.

21.2. PROBLEMS WITH THE BIG BANG 847 Horizon: greatest distance from which light could have reached us since the big bang (a) Earth Observable Universe Object presently inside the horizon. It can be seen from Earth Earth Object outside the horizon. It cannot be seen from Earth because light from it has not had time to reach us since the big bang. Earth's horizon Part of the Universe that both the Earth observer and distant observer can see (b) Horizon increases with time Earth (c) Distant observer Distant observer's horizon Earth The object that was outside the horizon now enters our horizon and is visible from Earth. (d) A and B are now outside of each other's horizons. This means they have always been outside of each other's horizons in the standard big bang model. A Earth B Horizon for A Earth horizon Horizon for B Figure 21.1: Horizons in an expanding universe. (a) A (cosmological) horizon is the greatest distance from which light could have reached us since the beginning of time. (b) Horizons expand with time, so objects currently outside our horizon may come within our horizon in the future. (c) Cosmological horizons are defined relative to each observer, so each has her own horizon. (d) Horizon problem produced by the CMB having identical temperatures on opposite sides of the sky for an observer: how do A and B know to have the same temperature if they could never have exchanged signals in the past?

848 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY Tiny change in initial conditions Scale factor Actual flat Universe Different tiny change in initial conditions Time Figure 21.2: The flatness problem: producing a flat Universe today requires remarkable fine-tuning of the initial curvature for the Universe. 21.2.2 The Flatness Problem Observational property 9(b) implies that the Universe is euclidean. This indicates that the Universe is very near the closure density. Consistent with big bang, but this condition can be realized only if parameters are very finely tuned in the early universe (Fig. 21.2). Example (Exercise): the fractional deviation of the density from the critical density at any time in the evolution of the Universe is ρ ρ = ρ ρ c ρ = 3kc2 8πGa 2 ρ, From this result, unless the flatness is tuned to one part in 10 60 at the Planck time we end up with a Universe that is far from flat today. While possible, this does not seem to be a very natural initial condition.

21.2. PROBLEMS WITH THE BIG BANG 849 Strong Strength of force E & M Weak Gravity GUTs scale Magnetic monopoles produced? Planck scale Temperature Figure 21.3: The magnetic monopole problem of the standard big bang: where are the massive relic particles that would be expected to be produced at phase transitions like grand unification (labeled GUTs)? 21.2.3 The Magnetic Monopole Problem There are reasons to believe that massive particles like magnetic monopoles could be produced copiously at phase transitions in the early universe, as illustrated in Fig. 21.3. This has two adverse consequences: Such particles have never been detected in experiments, and If they were produced in large numbers they would have halted the expansion of the Universe and then caused it to collapse. These problems are removed if we simply declare that such particles are not produced in large numbers, but why should such an initial condition be required?

850 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.2.4 The Structure and Smoothness Dichotomy Observational properties (4) and (8) (smoothness of CMB vs. existence of large-scale structure) present a severe compatibility issue: The remarkably high smoothness of the CMB implies that the early Universe was strikingly devoid of density perturbations. Where then did the density perturbations responsible for the growth of rich structure in the present Universe on the supercluster and smaller scale originate? The form of the density perturbations required to give the observed structure is known so they could be postulated as initial conditions, but again we would like to know why.

21.2. PROBLEMS WITH THE BIG BANG 851 21.2.5 The Vacuum Energy Problem Observation 9(a) (accelerated expansion) has a simple explanation only if the Universe contains dark energy. This would be most naturally explained if dark energy is a consequence of vacuum fluctuations. However, estimates of the vacuum energy content of the Universe are spectacularly wrong in comparison with the corresponding observational constraints. The accelerated expansion is consistent with the big bang picture if we simply postulate the existence of dark energy in the Universe in the required amount. But it is highly unsatisfying to have no understanding of where this fundamental influence on the evolution of the Universe comes from.

852 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.2.6 The Matter Antimatter and Baryogenesis Problem Observation (8) indicates that the physical universe contains almost entirely matter with little corresponding antimatter. We can impose this as an initial condition but that is bothersome given that matter and antimatter enter modern elementary particle physics theory on an equal footing. A closely-related problem (because annihilation of baryons with antibaryons produces photons) is how to account for the large excess of photons over baryons in the Universe (Observation 7).

21.2. PROBLEMS WITH THE BIG BANG 853 21.2.7 Modifying the Classical Big Bang We shall now discuss some possible resolutions of these problems. In attempting to resolve the problems we have to be careful to preserve the successes of the big bang model. The successful predictions of the big bang model rest primarily on the evolution of the Universe at times later than about one second after the initiation of the big bang. Therefore, any modification of our cosmological model that influences the Universe at times less than about one second after the big bang will leave the successes of the big bang intact if they leave appropriate initial conditions for the subsequent evolution. We begin with a proposed modification of the evolution of the Universe operative only in the first tiny fraction of a second of the big bang that has the potential to resolve the first four problems listed above in a single stroke.

854 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.3 Cosmic Inflation The theory of cosmic inflation is based on a simple but striking idea that has been discussed already in conjunction with the de Sitter solution: In the presence of an energy density that is constant over all space, the Einstein equation admits an exponentially growing solution. If the Universe underwent a short burst of exponential growth before settling down into more normal big bang evolution, there would be potentially large implications for the evolution of the Universe. We shall take the essential point of inflation to be this general idea of the Universe experiencing a period of exponential growth. There are many specific versions of inflationary theory that implement this in different ways. For the most part we shall leave those specifics for the interested reader to pursue in the specialist literature. Our reason is that there is now compelling evidence that the basic idea of inflation is necessary to explain the evolution of the early Universe, but no specific version of inflation currently available gives a completely satisfactory accounting of the cause and detailed effects of the inflationary period.

21.3. COSMIC INFLATION 855 21.3.1 Inflationary Theory From earlier discussion of the de Sitter solution, A universe with pure vacuum energy expands exponentially, a(t)=e Ht, where the Hubble parameter H is constant. The basic idea of inflationary theory is that shortly after its birth the Universe found itself in a situation dominated by a constant (or nearly constant) energy density. This drove an exponential expansion for a very short period of time that cooled the Universe rapidly because of the expansion. Then at the end of this period the Universe exited from the inflationary conditions and reheated. The mechanism for reheating depends on the version of inflation assumed, but generally involves the rapid conversion of the constant energy density driving inflation into the mass energy of more normal particles). This then produced a situation dominated by radiation rather than vacuum energy, which caused the Universe to evolve according to a standard (hot) big bang scenario (power law rather than exponential dependence of the scale factor on time).

856 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY In various versions of inflation different reasons are assumed for the initial conditions that triggered the exponential expansion. The original inflationary idea due to Alan Guth assumed that inflation was driven by a Lorentz scalar field associated with a first-order phase transition. This is conceptually simple, but proved to be incompatible with observations (as Guth himself realized). It was found that the resulting inflation could not halt in a manner that would give something that looks like the real Universe. In subsequent versions of inflation the inflation was often assumed to be driven by a scalar field having a time dependence of a particular form called a slow rollover transition. Although such theories often give a reasonably good account of data, they suffer from 1. having little connection to scalar fields known already to exist in elementary particle physics, and 2. requiring extremely fine empirical tuning of parameters to account well for data. In keeping with the philosophy outlined above, we omit discussion of these different forms of inflation and instead concentrate on the consequences of inflationary expansion.

21.3. COSMIC INFLATION 857 (a) 10-32 s (b) Hot big bang? Hot big bang a Inflation ~10 50 T 2? No inflation Inflation Reheat Time Time Figure 21.4: The inflationary scenario. (a) In the inflationary epoch the Universe expands exponentially, which can increase the scale factor by factors of 10 50 or larger on a timescale of order 10 32 s. (b) The Universe cools as it expands exponentially. At the end of inflation some mechanism, not yet well understood, must reheat the Universe, which then continues a standard hot big bang evolution. Figure 21.4 illustrates the behavior of the scale factor and the temperature in highly schematic fashion during inflation and the following big bang evolution. During inflation the Universe expanded at a much higher rate than in normal big bang evolution. At the same time, the temperature dropped rapidly in the exponentially expanding Universe. Finally, when the period of inflation halted the Universe first rapidly reheated and then began to decrease in temperature according to the standard big bang scenario. The question marks represent our substantial lack of knowledge concerning the Universe prior to the inflationary period.

858 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 1 2 Eventual location of Earth Causally-connected, homogenous region Horizon Inflation Standard big bang evolution 1 Horizon 2 Inflationary universe expands faster than the horizon Horizon expands faster than big bang universe 1 Reenter horizon 2 In inflation an original small, homogeneous region expands much faster than does the horizon distance. Then when inflation ends and normal big bang evolution begins, the horizon expands faster than the Universe. Figure 21.5: Solution of the horizon problem in the inflationary universe. 21.3.2 Taking the inflationary cure The inflationary scenario provides (in principle) a solution to the four fundamental problems posed above. Solution of the Horizon Problem The solution of the horizon problem is illustrated in Fig. 21.5. The tremendous expansion means that regions that we see widely separated in the sky now at the horizon were much closer together before inflation. Thus, they could have been in contact by light signals.

21.3. COSMIC INFLATION 859 Solution of the Flatness Problem The tremendous expansion greatly dilutes any initial curvature. Think of standing on a basketball. It would be obvious that you are standing on a two-dimensional curved surface. Now imagine expanding the basketball to the size of the Earth. As you stand on it now, it will appear to be flat, even though it is actually curved if you could see it from large enough distance. The same idea extended to four-dimensional spacetime accounts for the present flatness (lack of curvature) in the space of the Universe. Out to the greatest distances that we can see the Universe looks flat on large scales, just as the Earth looks approximately flat out to our horizon.

860 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY Solution of the Monopole Problem The rapid expansion of the Universe tremendously dilutes the concentration of any magnetic monopoles that are produced. Simple calculations indicate that they become so rare in any given volume of space that we would be very unlikely to ever encounter one in an experiment designed to search for them. Nor would they have sufficient density to alter the gravity and thereby the normal expansion of the Universe following inflation.

21.3. COSMIC INFLATION 861 Subatomic scale Vacuum Time Particle Antiparticle Vacuum Figure 21.6: Quantum fluctuations can create a particle-antiparticle pair from the vacuum for a fleeting instant. In inflation such microscopic fluctuations can be stretched to macroscopic scales, producing density perturbations that can later seed the formation of large-scale structure. Inflation and the Formation of Structure Perhaps the most important consequence of inflation is that it provides a possible solution to the origin of large-scale structure. The inflationary explanation is in fact rather remarkable. During inflation quantum fluctuations such as that illustrated in Fig. 21.6 (which must be present because of the uncertainty principle) end up being stretched from microscopic to macroscopic dimensions by the exponential expansion. Because this process occurs during the entire time of inflation, one ends up with density fluctuations of macroscopic size varying over many length scales.

862 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY Technically, this produces what is termed a scale-invariant spectrum of density fluctuations, and it is known empirically that this is the spectrum of density perturbations that is most likely to lead to the observed large-scale structure in the Universe. These density perturbations will generally be expanded beyond the horizon during inflation. But after inflation is over and normal big bang evolution sets in, the horizon grows with time. Eventually these density perturbations come back within the horizon where they can serve as nucleation centers for the formation of structure.

21.3. COSMIC INFLATION 863 Angular wavelength (degrees) 80 180 20 5 2 1 0.5 0.2 Temperature fluctuation (µk) 60 40 20 Inflation with dark energy Inflation with no dark energy Open universe, no inflation, no dark energy WMAP CBI ACBAR BOOMERANG 0 2 10 40 100 200 400 600 800 1000 1200 1400 1600 1800 Multipole order Figure 21.7: Temperature fluctuations in the cosmic microwave background from satellite and high-altitude balloon observations compared with various theoretical models. Although there are many specific theories of inflation, it is encouraging that simulations of large-scale structure give reasonable results when the effects of inflation are included. Furthermore, the fluctuations in the CMB observed by WMAP are described best by theories that include the effect of inflation. For example, Fig. 21.7 compares the angular fluctuations in temperature for the CMB with various models with and without inflation and with and without dark energy. Models with both dark energy and inflation are clearly favored.

864 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY 21.3.3 Inflation Doesn t Replace the Big Bang Inflation is not a theory in competition with the big bang: The theory of inflation modifies only the first tiny instants of creation. After the completion of the brief period of inflation, it is assumed that big bang evolution continues as described earlier. Thus, inflation should be viewed as a modified form of the big bang that accounts for effects due to the properties of elementary particles that are not included in the standard big bang.

21.4. THE ORIGIN OF THE BARYONS 865 21.4 The Origin of the Baryons In the standard big bang the preponderance of matter over antimatter and of photons over baryons in the Universe have to be introduced through initial conditions without fundamental justification. Sakharov first enumerated the ingredients required to generate baryon asymmetries within the standard big bang model: 1. There must exist elementary particle interactions in the Universe that do not conserve baryon number N B. 2. There must exist interactions that violate both charge conjugation symmetry (C) and the product of charge conjugation and parity (P) symmetries (the product is denoted CP). 3. There must be departures from thermal equilibrium during the evolution of the Universe.

866 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY In these requirements Baryon number N B takes the value +1 for a baryon and 1 for an antibaryon. Baryon number is then the algebraic sum of these numbers for all the particles in a reaction. Conservation of baryon number (observed in every experiment done so far) means that this number does not change in the interaction. Charge conjugation symmetry (C) is symmetry under exchange of a particle with its antiparticle. Parity symmetry (P) is symmetry under inversion of the coordinate system through the origin. CP symmetry is symmetry under inversion of the coordinate system and exchange of particle with antiparticle. Most interactions conserve these symmetries to high precision but the weak interactions are known to violate P, C, and CP.

21.4. THE ORIGIN OF THE BARYONS 867 Departures from thermal equilibrium are likely to have occurred at various times in the evolution of the Universe. At least the weak interactions are known to violate both C and CP symmetry. Thus (in principle) all ingredients exist to account for baryon asymmetry except for baryon non-conserving reactions. Experimentally, baryon non-conservation has never been observed. However, there are theoretical reasons to believe that baryon conservation might not be an exact symmetry but just one that has not yet been observed to be violated. For example baryon non-conservation may occur only on a energy scale not yet reached in laboratory experiments but that could have occurred in the early Universe.

868 CHAPTER 21. EXTENDING CLASSICAL BIG BANG THEORY One class of elementary particle theories that features baryon-number violating interactions prominently and thus could have played a role in producing the baryons is that of Grand Unified Theories (GUTs). In the Standard Electroweak Theory of elementary particle physics the electromagnetic interactions and the weak interactions have been (partially) unified. This means that at high enough energy (in this case a scale of about 100 GeV, where a GeV is 10 9 ev) the weak and electromagnetic interactions take on the same properties. A GUT attempts to extend this idea to unify weak, electromagnetic, and strong interactions into a single unified theory. The characteristic GUT energy scale is very high (10 14 15 GeV is a common estimate), but on that scale GUTs typically violate baryon number strongly. At one time GUTs were favored as the likely way to account for baryogenesis but there have since been shown to be difficulties with this approach. In particular, it seems that a baryon asymmetry generated by a GUTs phase transition would likely be wiped out by the cosmic inflation described earlier. Thus a viable theory of baryon asymmetry may require a baryonviolating phase transition at a lower energy scale than the GUTs scale.

21.4. THE ORIGIN OF THE BARYONS 869 A possible alternative mechanism is leptogenesis. Leptogenesis postulates that perhaps the baryon asymmetry was generated by strongly CP-violating processes in the electroweak sector. But it is not clear that this can account for the observed baryon asymmetry of the Universe because the known electroweak interactions do not exhibit interactions with the required characteristics. However, the correct electroweak theory could be more general than the present one (which is not tested exhaustively at energies of 100 GeV or larger, and is now known to be contradicted by the small but finite masses observed for neutrinos). Thus, an improved electroweak theory eventually might be able to account for the baryon asymmetry.