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).
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.