Something becomes visible when it interacts with
light in such a way that we can see it. Astronomers studying the motions
of stars in spiral galaxies noticed that the mean star velocity did
not drop off with radius from the galactic center as rapidly as the
falloff in luminous mass in the galaxy dictated according to Newtonian
gravity. The stars far from the center were rotating too fast to be
balanced by the gravitational force from the luminous mass contained
within that radius. This led to the proposition that most of the mass
in a galaxy was low luminosity mass of some kind, and this invisible
mass was called dark matter.
Dark matter is probably not baryonic matter, because
the abundance of primordial elements such as hydrogen, helium and deuterium
would be much higher if the Big Bang had produced enough baryon density
to account for the dark matter in galaxies.
The amount of dark matter present in the Universe
has been estimated using various techniques, including observing the
velocities of galaxies in clusters and calculating the gravitational
mass of galactic clusters by their gravitational lensing effects on
surrounding spacetime. The end result is that the baryonic density W_{B}
is about 5% and the dark matter density W_{D}
is about 30%
The leading candidate for dark matter right now comes
from supersymmetry.
Supersymmetric versions of the Standard Model of elementary particle
physics contain heavy supersymmetric partners of the electroweak gauge
bosons and the Higgs field that are electrically neutral and hence don't
interact with electromagnetic radiation, aka light. These neutralinos,
as they are called, are fermionic partners of the neutral gauge bosons
and the Higgs field. They would have high mass, yet interact very weakly,
and those two qualities make them a good candidate for dark matter.

The Cosmological Constant

The observational evidence that the Universe was
expanding didn't come around until 1929, which was 14 years after the
Einstein's General Theory of Relativity was first published. The Einstein
equations predicted an expanding Universe for any kind of ordinary matter
or radiation in existence.
There being no evidence yet to make people believe
that the expanding solutions to the Einstein equations represented observed
physics, Einstein postulated a new kind of energy density that could
balance the matter density in the Universe and prevent the Universe
from expanding. This new theoretical energy density is called the cosmological
constant, known by the symbol L.
The energy density and pressure for L
are

The Einstein equations with a matter density r_{m}
and cosmological constant L become

A static solution has a(t) = constant = a_{0}, which means
that k=+1 and the matter density, cosmological constant L_{0}
and scale factor are related by

A cosmological constant alters the time evolution
that is associated with a given spatial curvature. The k=+1 spacetime
with only matter expands and then recollapses, but the k=+1 spacetime
with matter and a cosmological constant can either expand forever (for
L > L_{0}),
stay the same forever (L = L_{0})
or expand and recontracts (0 < L
< L_{0}).
If L > 0
and k= 0 or -1, then space expands forever. If L
< 0, then k=-1. When k=-1 with matter and no cosmological constant,
the Universe is open and expands forever. But for L
< 0, even though k=1 and the topology of space is open, this spacetime
expands and then recontracts like the k=+1 model with matter and no
cosmological constant.

What's the final answer?

1. Our Universe is pretty
flat: The cosmic microwave background is the relic of Big Bang
thermal radiation, cooled to the temperature of 2.73° Kelvin. But
it didn't cool perfectly smoothly, and after the radiation cooled, there
were some lumps left over. The angular size of those lumps as observed
from our present location in spacetime depends on the spatial curvature
of the Universe. The currently observed lumpiness in the temperature
of the cosmic microwave background is just right for a flat
Universe that expands forever. 2. There is a cosmological
constant: There is a vacuum energy, or something that acts just
like one, to make the Universe accelerate in time. The acceleration
of the Universe can be seen in the redshifts of distant supernovae. 3. Most of the matter in
the Universe is dark matter: Studies of galactic motion show
that ordinary visible matter in stars, galaxies, planets, and interstellar
gas only makes up a small fraction of the total energy density of the
Universe.
The Universe at our
current epoch has (approximately)

So right now the density of vacuum energy in our Universe is only about
twice as large as the energy density from dark matter, with the contribution
from visible baryonic matter almost negligible. The total adds up to
a flat universe which should expand forever.