3.1. Dark matter
In the 1970s the need to advocate for the existence of a considerable quantity of dark matter (DM) in the universe was clearly established. The measurement of the Doppler shifts of star light in the external parts of the spiral galaxies shows an unexpected behaviour: The velocities of stars (or HII regions) orbiting around the galactic center did not decrease following the foreseeable Keplerian dynamical behaviour (Rubin & Ford 1970), but instead remained roughly constant to great distances from the galactic center. The presence of dark matter in the galactic dynamics was used for rescuing the works of Fritz Zwicky of the decade of 1930 from the oversight. Zwicky had to advocate the existence of this type of matter (dunkle Materie) to maintain the stability of the galaxy clusters (Zwicky 1933) 1. The measurements of the average peculiar velocity dispersion in the radial direction with values of the order of 1000 km/sec in the Coma cluster led Zwicky to this conclusion. The velocities of galaxies within the cluster are a consequence of the gravitational potential associated to the total cluster mass. In this kind of virialized systems, the potential energy is related with the kinetic energy, - associated to the distribution of individual galaxy velocities - through the virial theorem (2K + U = 0), providing a method to estimate the total cluster mass.
Other observations carried out in the 1980s, as the emission in X-rays produced by the hot gas in clusters of galaxies or the image distortions and magnifications produced by galaxy clusters acting as gravitational lenses, have corroborated the need for dark matter.
It is essential to distinguish two aspects: existence and nature, with the former quite firmly established and the latter much constrained but still unknown. One can, in a sense, regard "dark matter" as a shorthand for a very large number of observations on many scales, indicating that mass to light ratios increase as you look at larger entities. This was pointed out in a pair of important and influential papers by Einasto, Kaasik, and Saar (1974) and Ostriker, Peebles, and Yahil (1974). These and other observations, when collectively plotted on a logarithmic scale of luminosity-to-mass ratio vs. the length scale, show a monotonic rise from unity for 1-parsec diameter young star clusters to something like 200-300 M / L for the largest superclusters of galaxies and other very large scale structures explored with weak gravitational lensing. The rise does not continue on larger scales, though many back in the 1980s thought it would. Such a plot could have been made before the Second World War, using Hubble's numbers for the inner parts of galaxies, Babcock's rotation curve for M31 (Babcock 1939), Holmberg's binary galaxies (Holmberg 1940), and the data on the Coma and Virgo clusters from Zwicky (1933) and Smith (1936).
More modern data include a still large range of systems - disks of galaxies from motions of stars and gas perpendicular to them, whole clusters from X-ray and lensing data, and the very largest scale information we have from the CMB, Type Ia supernovae, and weak gravitational lensing. The only possible conclusions are either that gravity becomes monotonically stronger on large scales or that the ratio of non-luminous matter increases with length scale. The latter is by far the majority view in the astronomical community and centers around something like 23% of the closure density being in non-luminous, non-baryonic dark matter.
A number of ideas in modern physics imply dark matter candidates, of which the most often sought is supersymmetric partners of known particles, the lowest-mass supersymmetric particle in 4-d space time or perhaps the lowest-mass Kaluza-Klein particle in 5-d space time. Current observations and experiments are looking for three manifestations: (1) photons or e± pairs produced when DM particles annihilate today, (2) scattering of the particles in large laboratory detectors (made of NaI crystals, very pure water, or other substances), and (3) production of DM particles in accelerators like the upcoming LHC. Other viable DM candidates include axions, black holes in a few unprobed mass ranges, topological singularities, and many more exotic entities. Remembering here, as in other places in this chapter, that theories are cheap but telescopes or accelerators are expensive, we encourage our theoretical colleagues to think broadly and to deduce possible detectable consequences of their DM-candidates, particularly consequences that might be found (like gamma ray emissions or positron excesses) in projects that are being carried out for other purposes. Very large investments in programs narrowly aimed at a single candidate are harder to feel positive about (White 2007).
3.2. Dark energy
Dark energy (DE), like dark matter, is a shorthand for a large number of observations and ideas. But in this case, an idea came first. The differential equations for a homogeneous, isotropic, relativistic universe are second-order, and so admit two integration constants. The first (in suitable units) is the Hubble parameter at some reference time. The second takes the form of a uniform density (always positive) and pressure (which can be positive or negative), with negative pressure tending to oppose ordinary gravity (McVittie 1956). Einstein called it and wanted it initially to permit a static universe (which turned out to be unstable). It is now generally written as , and Einstein left it out of his publications after 1930. In 1934, however, R.C. Tolman included the possibility of both positive and negative values of , and one of his model universes, with negative pressure , expanded from a singularity to infinite size, with an empty de-Sitter universe as its limit.
Despite the frequent phrases "Einstein's infamous cosmological constant" and "Einstein's worst blunder," has never entirely disappeared from the literature, serving in at least a few minds as a solution to the problem presented by a universe somewhat younger than its contents, a problem never entirely eliminated by recalibrations of the Hubble constant between 1952 and the present. De Vaucouleurs, for instance, always included in his cosmological discussions, beginning in about 1956. There was another revival around 1970 in connection with the apparent excess of QSOs with redshifts close to 1.95. Eventually regarded as a selection effect, this could, in principle, have been a signature of a coasting phase in an open universe with non-zero . Incidentally, the critical density case (now thought to be very close to reality) has no coasting phase, only an inflection point in the expansion parameter a(t).
Observational cosmology, gradually involving many more kinds of observations than just Sandage's "search for two parameters" proceeded apace, and by the time of the 1997 IAU General Assembly in Kyoto, evidence had accumulated from large scale structure, galaxy formation simulations, ages, and big bang nucleosynthesis for a flat (critical density) universe with something like 70% of the gravitation coming from negative-pressure . Since then, the numbers favoured by several panel members there (4-5% baryons, 23-25% dark matter, and the rest ) have been reinforced by results of studies of weak gravitational lensing, supernovae, and angular fluctuations of the CMB seen by WMAP.
For many decades cosmologists have been trying to quantify how the expansion of the universe discovered by Hubble (1929) was slowing down due to gravity. However, in 1998, two independent teams (Riess et al. 1998, Perlmutter et al. 1999) presented convincing evidence for just the contrary: an accelerated expansion. They used high-redshift Type Ia supernovae (SNe Ia) as standard candles (Phillips 1993). The behaviour of its calibrated luminosity-distance as a function of the redshift of their host galaxies ruled out the Einstein-de Sitter spatially flat cosmological model, indicating that the cosmic expansion had been speeding up during the last 5 Gyr or so. was then definitively rescued from the wastebasket in 1998 with the interpretation of the luminosity-distance-redshit relation of very distant type Ia supernovae as evidence for acceleration in cosmic expansion. The two mentioned teams analyzed a set of high-z supernovae and found them fainter than expected. After ruling out possible systemic obscuration by dust or evolutionary effects, they interpreted the dimmer luminosity as a consequence of being farther away, and thus implying an acceleration in the expansion.
At this point, physicists step into the picture, asking "what is apart from the integration constant that Einstein called it? 2" And "why does it have the numerical value we find?" New words, especially dark energy and quintessence, are invented to describe it and to suggest the possibility of variation with time and perhaps space. It acquires an equation of state: p = w, where w exactly and always -1 is just back again, therefore the simplest form of dark energy is the stress-energy of empty space - the vacuum energy - , which is mathematically equivalent to the Einstein's cosmological constant, but other values of w and time variability might allow eventually recontraction of the universe or expansion so fast that it tears. These other forms of dark energy that dynamically evolve with time have been considered in the literature (Peebles & Ratra 2003) and are called "quintessence". The astronomical community has embraced very quickly the idea of accelerated expansion. The solid arguments accompanying the observations of the SNe Ia have been confirmed with spectroscopic analyses (Bronder et al. 2008, Sullivan et al. 2009) that test for possible systematic uncertainties. Their results confirm the reliable use of SNe Ia as standardized candles. Moreover, there exists other independent observational evidence supporting the accelerated expansion of the universe. For a review see Frieman et al. (2008). Amongst these probes, one of the most promising techniques is the measurement of the baryon acoustic oscillations (BAOs) in the large-scale distribution of matter in the universe (Eisenstein et al. 2005, Cole et al. 2005, Martínez et al. 2008).
Dark energy in this modern sense has been associated with the last gasp of inflation, new scalar fields, vacuum field energy, and other innovative physics that we do not pretend to fully understand. The catch in most cases is that the natural amount should have a density of one Planck mass (10-5 g) per Planck volume (10-99 cm3), something like 10120 larger than the 73% of closure density implied by the concordant observations of supernovae, the CMB, large scale structure, etc.
1 Zwicky was not, however, the first either to use the phrase dark matter or the first to report a number for it. James Jeans (1922) and Jacobus Kapteyn (1922) estimate the mass in the disk of the Milky Way (by method refined by Jan Hendrik Oort in 1932), reporting the presence of dark stars. Back.
2 In a letter to Besso quoted by Kragh (1996), Einstein explained: "Since the universe is unique, there is no essential difference between considering as a constant which is peculiar to a law of nature or as a constant of integration." Back.