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1z Highlights BIG-BANG NUCLEOSYNTHESIS At present, the relics of the big bang that provide the most informa- tion about the early universe are certain light nuclei, such as deuterium (D) and 4He. Calculations of their production in the early universe are based on measured nuclear cross sections and rely heavily on quanti- tative details of the cosmological model. A few minutes after the origin of the universe, conditions of temperature and density were appropri- ate for the fusion of protons and neutrons to form nuclei of light ele- ments. Deuterons formed first, but the fusion reactions ran rapidly toward 4He because of its much greater stability. The amount of 4He produced depends essentially on two factors: the density of baryons (neutrons and protons) and the universal expansion rate at the epoch when the temperature dropped to ~109 K (t ~ 3 min). The baryon density at T~ 109 K can be computed from the present baryon density and the present temperature of the background radiation; and the expansion rate can be calculated for isotropic, homogeneous cosmo- logical models provided that the number of species of light particles is known. Hence precise predictions of the 4He abundance can be made; the calculated value lies in the range of 23-27 percent by mass. This agrees with the solar value and with the abundance found on old stars and in the interstellar medium, after correcting for the 4He made in stars. The fact that the predicted abundance of 4He agrees with the 90
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HIGHLIGHTS 9 1 RAT 10 OF BARYONS TO PHOTONS 10-'° 10-9 lo-8 10-7 .26 .22 .18, 10-31 ~ 10 5 11 c'' 10 7 In Cat 10 9 10" _ 4He - Few Observed ~ Pred i cted _ ~ D+3He _ ~ _ . 1 _ ~ ~ - AL; , , _ 3He \D \~ 0-32 1 o-3 10-32 10-31 10-3° lo-29 10 28 PRESENT BARYON DENSITY (g/cm3) FIGURE 12.1 Isotopic abundances compared with predictions of the standard big-bang model (black curves). Shaded areas indicate observed abundances for 4He, deuterium, 3He, and 7Li, which all show remarkable agreement with theory for a baryon-to-photon ratio in the range 10-'° to 10-9. Observed value provides the best evidence for the validity of the standard big-bang model at these early times. Even more has been learned from studies of light-element abun- dances. While the 4He abundance is not a strong function of the density of baryons, the small residual D abundance depends sensitively on this quantity, being relatively larger for lower baryon density. Figure 19. 1 shows the predicted primordial abundances of several light nucleic as functions of the present baryon density- a poorly known cosmological parameter. The observed abundances are shown by shaded rectangles, with 7Li being a recent addition. The agreement with predictions is striking and suggests a present baryon density of 3 x 10-3 g/cm3. This
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92 COSMOLOG Y density is 1 or 2 orders of magnitude less than the density required to close the universe, that is, to stop the current expansion and cause recollapse. It also may be less than the density required to explain the observed dynamics of large clusters of galaxies. Thus, suspicion is rising that the long-sought invisible (sometimes called missing or dark) matter is something other than baryons. We return to this point below in the section on Invisible Mass. One might suppose that the observed light nuclei were produced by much later astrophysical processes, making the agreement in Figure 12.1 fortuitous. At this point we know that these light nuclei cannot be produced by the collisions of cosmic rays with the interstellar gas and that no other production mode has been found for D. Thus, the deuterium abundance is particularly important. The sensitivity of the production of 4He to the expansion rate of the universe at t ~ 3 min has allowed constraints to be placed on other physical parameters. For instance, if more than a few types of neu- trinos exist, the expansion rate would have been greater, resulting in excessive production of helium. Also, if the gravitational "constant" had been different at that early epoch (G/G ~ 0), the expansion rate and the helium production would have been altered. Finally, the uni- verse could not have been very anisotropic at t = 3 min. because that would also have increased the average expansion rate. LARGE-SCALE PROPERTIES OF THE UNIVERSE The general expansion and deceleration rates of the universe have been a central focus of cosmology for the past 30 years. Recent work has narrowed the uncertainty in Hubble's constant, a measure of the current expansion rate (Ho = 50 to 100 km/s per Mpc*), but the deceleration parameter q0t remains poorly known. The classical meth- ods to study the geometry of space-time use visible galaxies and radio sources as coordinate measures. Usually, source intensity is used as a measure of distance, but this requires a knowledge of time dependence of the source luminosity and spectrum. The effects of source evolution have not yet been sufficiently well understood to permit a geometrical * 1 megaparsec (Mpc) ~ 3 x 106 light-years, roughly 1/5 the spacing between large galaxies. t In the simplest big-bang models (pressure = 0, cosmological constant = 0) q0 = t/2Pmeasure~/Pcri~ica~. For q ~ 1/2 the universe is open and expands forever; q > 1/2 means our universe is closed and will recollapse. Measurements of the density p and deceler- ation qO of the universe are of major importance to cosmology.
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Lo ~ ~ - HIGHLIGHTS 93 FREQUENCY (G He 40 4 . . . . . . MICROWAVE BACKGROUND SPEC T R U M _ 10 14 _ :r - - ~n ~ 10 46 cot cot
94 COSMOLOGY at that epoch. Einstein's major cosmological assumption of large-scale homogeneity and isotropy seems well justified. Incidentally, there is an interesting noncosmological feature in the anisotropy of the 3-K radiation- the dipole erect. It arises from the Earth's motion through the radiation and measures our velocity relative to the reference frame of the radiation, assumed to be the same as that of matter at large distances. The inferred velocity of our galaxy is surprisingly large and suggests that we are being perturbed by local mass concentrations such as the Virgo cluster of galaxies and its surroundings. Failure to observe a quadrupole anisotropy with an amplitude larger than 10-4 K provides an important constraint on homogeneous but anisotropic cosmological models. Such models are completely consis- tent with general relativity, and indeed the number of such models is much larger than the number of isotropic models. Nevertheless, ob- servations of the isotropy of the background radiation, and the agreement of the predicted and measured abundances of light-element abundances, tightly restrict the range of possible anisotropic models. Finally, the high degree of isotropy in the 3-K radiation raises a serious causality question. In the standard model, regions separated in the sky by more than ~1 degree were not yet causally connected at z ~ 103, the epoch of last scattering (assuming no reionization). How then did the photons coming from those regions manage to have the same temperature, to 1 part in 104? This long-standing problem with the 3-K radiation in the simple model may be solved by a fascinating new idea the inflationary universe discussed below in the section on The Inflationary Universe. STRUCTURE IN THE UNIVERSE The clumping of matter in the universe into galaxies, clusters of galaxies, and still larger structure is currently under intense scrutiny. Quantitative observational work has rapidly accelerated with new developments in detector and data-processing technology. Analyses of angular distributions of galaxies on photographic plates are now complemented by three-dimensional information from the first large- scale statistical samples of galaxy redshifts.* Redshift measurements require spectra, so they take much more time to obtain than do * The redshift gives the recession velocity, which is related to the distance by Hubble's law v = Hod.
HIGHLIGHTS 95 photographs, but redshift surveys yield a much clearer picture of the galaxy distribution and dynamics. On small scales (~10 Mpc) the galaxy distribution approximates a scale-invariant fractal within which there is an occasional great cluster of galaxies. On larger scales one finds a complex pattern of superclusters, clouds, voids, and filaments of galaxies. There is considerable theoretical and observational activity devoted to tracing the evolution of this structure back to its origins. Evidence exists that radio sources, quasars, and perhaps also galaxies have changed appreciably between the epoch z ~ 3 and the present. But the burst of radiation that may accompany galaxy formation at an epoch somewhere between z ~ 3 and z ~ 100 has not yet been seen. Indeed, so little is known about the formation and development of structure in the universe that we are currently debating whether stars or large clusters of galaxies formed first. Galaxies and clusters of galaxies may arise from small density fluctuations, Ap/p, in the early universe. Two limits can be set on the magnitude of fluctuations at the time of decoupling of matter and radiation. Since the current density contrast on the scale of clusters of galaxies is about unity, and gravity causes Pip to grow as (1 + z)-i, the perturbations at z ~ 103 should be pip ~ 10-3. Another limit comes from the search for small-scale anisotropy in the 3-K radiation, which is a probe of roughness on the z ~ 103 surface. At angular scales corresponding to the sizes of large clusters (a few arc minutes) no fluctuations are seen down to ATIT~ 2 x 10-5. Current results of isotropy measurements of the 3-K radiation are shown in Figure 12.3. Under certain assumptions about the character of the fluctuations these two ways of estimating Ap/p are in conflict. For example, adi- abatic perturbations (favored by some models, especially those derived from particle-physics considerations) give pip ~ 3AT/T. Then the density contrast seen today Pip ~ 1) implies ATIT~ 3 x 10-4 at z ~ 103. But the limits shown in Figure 12.3 at scales of a few arcminutes are ten times smaller. There are several ways out of this dilemma: make the perturbations isothermal, clump the matter by forces other than gravitational (e.g., by supernova explosions), or rescatter the 3-K photons from an intermediate screen of electrons at z ~ 103. A recent idea suggests that nonbaryonic, invisible matter (e.g., anions, photinos, or massive neutrinos) can become nonrelativistic and begin to clump before z ~ 103. Baryons then fall into these clumps after decoupling from the radiation. Thus, there is ample time for structure to form in the invisible matter, and baryonic matter and microwave photons can be very weakly perturbed at decoupling. This is only one of the many ways that newly suggested particles
96 COSMOLOG Y lo-3 - lo 4 10-5 Anisotropy of 2.7 K Radiation Dipole ( 95 % Conf i dence Leve I s ) ~ ~ \ 10 30 1 3 · \ \ / ~ \ ~ T/? 1? ~ ~ ~ l l ll 1 0' 301 1 ° 3° ,,, , I 1 1, 1 0 ° 30° 90° 180° Angular scale 10 1.0 0.1< .01 FIGURE 12.3 Current results of searches for anisotropy in the cosmic microwave background radiation. The only effect seen, so far, is the dipole, which is due mainly (and perhaps totally) to our velocity through the radiation. Various symbols denote different observational techniques. Generally, small balloonborne instruments are used at angular scales larger than 3 degrees' and ground-based radio telescopes are used at smaller angular scales. . have been used to try to solve certain cosmological problems. On the other hand, the universe is a good laboratory in which to try out the properties of new particles. For example, the various candidates for invisible matter have different clustering properties. Some can form seeds for structures in the matter; others can provide a smooth mass density to help close the universe. Thus, cosmological observations can place constraints on the properties and abundances of new kinds of particles. INVISIBLE MASS The dark-matter problem is not new to cosmology. Observations since the 1930s have indicated that the mass density of visible matter (stars and gas) is insufficient to close the universe or to explain the dynamics of large clusters of galaxies, and recently it has become apparent that the visible mass cannot account for the strength of the gravitational field in the outer parts of galaxies, as indicated by the motions of stars and by the concentration of plasma around some galaxies. The discrepancy between what is observed directly as visible mass and what is indicated by dynamical measurements ranges from a factor of 2 in our stellar neighborhood to a factor of about 5 in galaxies
HIGHLIGHTS 97 to a factor of 30 or more in clusters of galaxies. This interesting trend for the invisible-mass fraction to increase with scale is not understood. With so much at stake, the search for the invisible mass is vigorous and extensive. Low-mass stars (mass ~ 0.1 MSun) are now unlikely candidates because galactic halos do not exhibit excess brightness at A = 2 ~m, where such stars are bright. Still lower mass objects ("Jupiters") are possible, since they are not luminous and hence are extremely hard to detect. Black holes are popular candidates for the invisible mass; and again, they are hard to find, especially in isolation. Currently, we are not even agreed that a black hole has been identified, though there are several excellent candidates among the known x-ray sources. Massive black holes (~108 MSun) are suspected as the "central engines" in active galaxies and quasi-stellar sources. Also, primordial black holes with masses down to 1O'5 g could exist and easily have escaped detection. (Those with masses below ~ 10'5 g are predicted to have evaporated by now by the Hawking process; see section on Quantum Particle Creation by Black Holes in Chapter 8.) Theoretical studies have taught us much about the astrophysical and relativistic properties of black holes, but we still do not understand how (if at all) such objects act as the powerhouses for active galactic nuclei or whether it is reasonable to assume that black holes might have existed in great numbers in the early universe. Their contribution to the invisible mass remains un- known. Since the dark-matter candidates mentioned so far are made from baryons, the nucleosynthesis constraint on baryon mass density has strong implications here. Stars, "Jupiters," and even black holes born after big-bang nucleosynthesis are included in the baryon density constraint noted in Figure 12.1- a density far short of that needed to close the universe. Thus, nucleosynthesis argues that one should look for nonbaryonic dark-mass candidates as a means to achieve closure density, Pc ~ 10-29 g/cm3. Several, yet unobserved, elementary particles are being proposed as dark-matter candidates. Already before reports of measured neutrino mass came from the Soviet Union, cosmologists had speculated about massive neutrinos as a source of nonbaryonic mass density. If neutri- nos have a rest mass of only a few electron volts, the thermal neutrinos produced in the hot big bang would dominate the mass density of the universe today. Although the reported measurement of neutrino mass is still controversial, it ushered in a flurry of theoretical activity resulting in even more invisible mass candidates. Axions were men- tioned earlier as possible seeds for galaxies; they are light pseudo-
98 COSMOf OGY scalar particles produced during the transition from quarks to hadrons that preceded primordial nucleosynthesis. Other new candidates are suggested by supersymmetric particle theories, which give partners such as the photino and gravitino to currently known particles. The virtually unconstrained richness of particle theory at very high energies can be expected to breed many invisible matter candidates. However, some constraints do exist. To help bind galaxies a relic par- ticle must have sufficient abundance today and must have become nonrelativistic so that gravitational clumping could take place. Also, the mass of any fermion candidate must be greater than the phase- space limit provided by the exclusion principle. ~ Some proposed particles have natural clustering scales that can be compared to observed structure, but it is still controversial which clustering lengths give the best fit to the phenomena. COSMOLOGY AND GRAND UNIFICATION A recent dramatic development in theoretical physics was the realization that the early universe is a useful laboratory for the testing of particle physics; conversely, new ideas in particle physics can be applied to some fundamental cosmological questions. Most interest has focused on an epoch when temperatures were high enough (T—1027 K or 1015 GeV) to possibly induce grand unification of three fundamental forces the strong, the weak, and the electromagnetic. An early suc- cess of this idea was to provide a possible explanation of the puz- zling asymmetry in the abundance of matter and antimatter in the universe, amounting to about one excess baryon (matter) per 109 photons. The standard cosmological model gives no clues, but Grand Unification Theories (GUTs) contain the necessary ingredients to answer this fundamental question. GUTs can be asymmetric with respect to particles and antiparticles, and they violate baryon conser- vation, producing a net baryon number in a universe that initially had equal numbers of baryons and antibaryons. The process occurs at a temperature corresponding to the rest-mass energy of the X boson (see Figure 11.1 in Chapter 11) which is responsible for the interconversion of quarks and leptons. Currently, particle experiments do not constrain the parameters of these theories nearly enough to allow an exact prediction of the baryon-to-photon ratio, although the detection of * Roughly, m4 > p~3 V-3, or m > 20 eV for typical densities and velocities inside a galaxy.
HIGHLIGHTS 99 proton decay would at least provide evidence that grand unification does occur at high energy. Thus, particle theory has provided a possible physical explanation for a fundamental cosmological property previously assigned to arbitrary initial conditions. Another important consequence of GUTs is the possibility of pro- ducing magnetic monopoles from singularities in the scalar (Higgs) fields invoked to generate particle masses. This could have occurred at the GUT era in the early universe, as regions with arbitrary alignments of the Higgs fields came into causal contact. In fact, in the simplest big-bang models far too many monopoles would have been produced; their present mass density would dominate the universe and cause excessive deceleration of its general expansion. This problem may be solved by a revolutionary idea that introduces into the early universe a process called inflation. THE INFLATIONARY UNIVERSE An ingenious way has been found to avoid the problem of excess magnetic monopoles emerging from the GUT era and to explain some older cosmological puzzles as well. The idea is that if scalar fields exist, their vacuum expectation value could provide a contribution to the mass density that remains constant in time, like the effect of the cosmological constant first introduced by Einstein. During the time following the GUT era when vacuum expectation energy dominates, the universe expands much faster than in the usual big-bang models, and this exponential expansion drastically dilutes the density of monopoles. The inflationary epoch must terminate, at least by the time of primordial nucleosynthesis, so that big-bang cosmology reigns during its successful epochs. According to current ideas, inflation ends when a lower (zero) energy state becomes accessible to the scalar fields as the universe cools by expansion. As noted earlier a particularly vexing problem with simple big-bang models is that regions of the universe having the same properties (radiation temperature, for instance) have never been in causal contact at the time we observe them. To explain the observed uniformity, one can invoke special initial conditions or quantum processes in the mysterious Planck era' but the inflationary model provides a specific alternative mechanism. In this picture, our entire observable universe is embedded in a larger region that grew from a single causally connected piece during the era of exponential expansion. Inflation also provides a possible way of understanding the flatness question, which basically asks: Why is the universe so close to a
100 COSMOf OGY balance between its kinetic energy of expansion and its gravitational binding energy? Considering the huge range of densities encompassed by the expansion, exceedingly fine tuning of this energy balance was required to allow the universe to reach its current state. The inflation picture explains this, again because of the enormous expansion factor. Indeed the model predicts a flat universe, which (for zero cosmological constant) has the current mass-energy density in the universe exactly equal to Pc, the critical closure density. At present, the study of the inflationary class of big-bang models is one of the most exciting areas within the rapidly growing union of theoretical particle physics and cosmology. But experimental support is needed; the discovery of the Higgs particles that produce the vacuum energy, for instance, would place inflation on much firmer ground. GRAVITATIONAL LENSES In 1979, an example of the long-predicted gravitational tensing was discovered. Multiple images of a quasar were formed by the bending of light in the gravitational field of an intervening group of galaxies. Such alignments are not so rare as one might think, because of the extreme distances to the quasars; six examples have been found to date. Cosmologists are intrigued because detailed geometric-optics calcula- tions of the paths have led to the possibility that the distribution of mass within the tensing system can be studied. In addition, if the quasar's luminosity varies with time, the different delays along the paths to the different images provide an additional scale, which in principle allows a determination of the distance to the intervening galaxies and thus the Hubble constant, Ho (see section above on Large-Scale Properties of the Universe). However, it may prove difficult to determine the properties of the tensing system well enough to realize this additional payoff.
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Representative terms from entire chapter: