2-1
c
Technical definition
In standard
cosmology, matter is anything whose energy density scales with
the inverse cube of the scale factor, i.e., ? x a-3. This is in
contrast to radiation,
which scales as the inverse fourth power of the scale factor ?
xa-4,
and a cosmological constant, which is independent of a. These
scalings
can be understood intuitively: For an ordinary particle in a cubical
box,
doubling the length of the sides of the box decreases the density
(and hence
energy density) by a factor of 8 (= 23). For radiation, the energy
density
decreases by a factor of 16 (= 24), because any act whose effect
increases
the scale factor must also cause a proportional redshift. A cosmological
constant, as an intrinsic property of space, has a constant energy
density
regardless of the volume under consideration.
In principle, “dark matter” means all components of
the universe which
are not visible but still obey ? x a-3. In practice, the term
“dark matter”
is often used to mean only the non-baryonic component of dark
matter,
i.e., excluding “missing baryons.” Context will usually
indicate which
meaning is intended.
2-2
Observational evidence
2-2
a
Galaxy rotation curves
Rotation
curve of a typical spiral galaxy: predicted (A) and observed (B).
Dark matter can explain the ‘flat’ appearance of the
velocity curve out to
a large radius.
The arms of spiral galaxies rotate around the galactic center.
The luminous
mass density of a spiral galaxy decreases as one goes from the
center to
the outskirts. If luminous mass were all the matter, then we can
model the
galaxy as a point mass in the centre and test masses orbiting
around it,
similar to the Solar System. From Kepler’s Second Law, it
is expected that
the rotation velocities will decrease with distance from the center,
similar
to the Solar System. This is not observed. Instead, the galaxy
rotation curve
remains flat as distance from the center increases.
If Kepler’s laws are correct, then the obvious way to resolve
this discrepancy
is to conclude the mass distribution in spiral galaxies is not
similar
to that of the Solar System. In particular, there is a lot of
non-luminous
matter (dark matter) in the outskirts of the galaxy.
