DARK MATTER
Since 1935 ( Fritz Zwicky ) it has been known
that there is a vast amount of unidentified, non-luminous matter in the
Universe. In the case of Zwicky he discovered this by looking at galaxies
in motion in clusters. The total mass needed to account for the motions
was about a factor of ten larger than could be accounted for by the sum
of luminous mass. We also see the same effect within galaxies, namely,
by measuring the velocities of stars as they orbit in the galaxy we can
use Kepler's law to determine the total mass contained within the star's
orbit. These so-called galactic rotation curves, we did the same thing
in class for our Milky Way Galaxy, reveal that there is far more mass within
the galaxy than can be accounted for by the luminous matter. Ordinary matter
is referred to as "baryonic" matter, i.e., it is composed of neutrons and
protons. Of course, neutral atoms also contain electrons( in the family
called leptons), but since the mass of the proton or neutron is 2000 times
bigger than the mass of the electron we use generically the term baryonic
matter for our ordinary matter.
Until about 1980 it was usually assumed that the unobserved mass was
ordinary baryonic matter present in some not easily detectable form, such
as gas, low mass stars, black holes, etc.. The most likely candidate is
called a Massive Compact Halo Object ( MACHOs). Since 1992 astronomers
have been looking for these objects using stars in the Large Magellanic
Clouds as a background to detect gravitational lensing caused by the MACHOs.
| Gravitational Lensing
of MACHOs
The rays of light from the star in the LMC are focussed by the relativistic effect of gravitational lensing. Thus, rays of light that would not have traveled to the observer can now get to the observer through the lensing effect. This makes the star brighten as the MACHO crosses the line of sight between the star and the observer. Once the MACHO has passed out of the line of sight the star returns to its former brightness. The MACHO is not seen itself. |
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MACHO events have been seen, but the numbers are too small to account
for all the dark matter.
We know from the success of the Big Bang nucleosynthesis (BBN) of the
light elements, hydrogens, heliums and lithiums, that the baryon density
is indeed larger than that deduced from luminous matter. However,
the density of ordinary matter required from BBN is still far smaller than
the density of mass seen in the Universe. This has led astrophysicists
to conclude that the vast bulk of the dark matter is in a form of non-baryonic
matter, referred to as Weakly Interacting Massive Particles, (WIMPs). WIMPs
are being sought in laboratory experiments, but so far there has been no
detection of them. These particles seemingly interact only through the
gravitational force. They are thus very different from the "ordinary" matter
of which we are made. In fact, since 90% to 99% of the mass in the universe
seems to be in the form of of dark matter, most of which is non-baryonic,
we should really be calling the dark matter "ordinary". As remarked by
B. Sadoulet ( reference below) the positive identification of WIMPs would
be another "Copernican" revolution. Not only are we not in the center of
the Universe, but we are also not made of the stuff of which most of the
universe is made!
Galaxy Formation
An additional need for the presence of dark matter arises when we try
to understand how galaxies were formed from the Big Bang. We assume that
clouds of primordial matter, mainly hydrogen and helium from BBN condensed
into galaxies and stars. It turns out that this condensation can not occur
unless there is sufficient gravitating mass. With the known value of the
Hubble constant telling us the expansion rate of the universe, the amount
of luminous matter seen is far too small to enable galaxies to form. The
formation of galaxies requires much more mass, and this is supplied by
the dark matter.
Although we ourselves, and our stars and planets are not composed of
non-baryonic matter, we could not exist without the presence of this non-baryonic
matter since stars would never have formed.
Galaxies form clusters , and these clusters form larger structures. Walls of galaxies stretching hundreds of megaparsecs across the sky are the largest known structures in the universe.
Inflationary Expansion
If the mass/energy in the universe were distributed in an absolutely smooth and uniform fashion during the early time of expansion then galaxies would not have formed. We recognize galaxies, or clusters of galaxies as "wrinkles" in the otherwise uniform cosmic "dust" of the universe. This clustering of matter could only occur if there were some initial variation in the matter density in the early universe. Only small initial deviations from uniformity are needed since the process of gravitational condensation will enhance the deviations, eventually leading to the large scale structure seen. A modern addition to the Big Bang theory is the "Inflationary theory". This theory predicts the correct temperature anisotropy seen in the cosmic microwave background radiation. The density fluctuations are the result of quantum mechanical fluctuations. This remarkable and successful prediction ties quantum mechanics to the field of cosmology. See the book by Alan Guth.
The Inflationary theory states that very near time zero of the universe
the universe underwent a very rapid expansion in size. This occurred near
time = 10-35 seconds at which point the universe shot out from
a size of about 10-52 meters to about 1 meter. In the
BB theory relying only on General Relativity the universe starts out at a size of about 10-7 meters
and expands to 1 meter by 10-35 seconds. In this
theory it had always been a puzzle as to why the cosmic microwave background
was so uniform. The level of uniformity requires that the
universe be in thermal equilibrium at the early stage. No matter which
way we look in the sky the CMBR is extremely smooth and the same( not counting
the tiny fluctuations that give rise to the galaxy formation above.)
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Imagine the universe to be a size d = 10-7 m. The temperatures in two different regions of the universe are Ta and Tb. In order for thermal equilibrium to exist Ta = Tb, and the only way this can happen is if photons can travel about in the universe conveying this information (i.e. Ta=Tb) all over. This means the universe has to be steady in size for a period of time long compared to the flight time of a photon across the universe. The time it would take a photon to cross this universe is about 3x10-16 seconds.. |
From the discussion in the box we see that the universe would have to
be stable in size for a time much greater than 3x10-16 seconds,
but in the standard BB theory the universe will have expanded enormously
in size in this time. Thus the photons couldn't keep up with the expansion
and there is no way other than by putting it in by hand to have the
uniformity in the CMBR we see. We say that the different parts of the universe
at temperatures Ta and Tb are "causally" disconnected. In the inflationary
theory the observed thermal equilibrium happens automatically since for
a value of
d = 10-52 meters the flight time for a photon is only 3x10-61
seconds, which is short enough that the universe appears static to the
photons. Thus, in the inflationary theory, the universe is automatically
in thermal equilibrium before the expansion starts. The inflationary expansion
simply brings to a large scale the thermal equilibrium that already existed.
Another prediction of the inflationary theory is that the universe is
effectively "flat". It will keep on expanding forever. Moreover, our observable
universe may be only a very tiny fraction of the "real" universe which
may be 1023 times larger.
The inflationary universe theory was originally proposed as an addendum
to the Big Bang theory. However, recently, it has become usual to view
the Big Bang theory as a component of inflationary theory. See the article
in the Scientific American Magazine by Andrei Linde. Our observable
universe, in this theory, is only one bubble in an ever expanding "Universe"
consisting of many bubbles. In fact, the values of the physical constants we see in our
own universe may not even be the same as those in other universes. The
discussion is somewhat reminiscent of "The Great Debate" at the beginning
of the 20th century about whether or not our galaxy was the whole universe
or whether the nebulae were really "Island Universes".
Cosmology at the millennium, Michael S. Turner, Reviews of Modern Physics 71(1999)S145
Deciphering the nature of Dark Matter, Bernard Sadoulet, Reviews of Modern Physics 71(1999)S197
Astronomy! A Brief Edition, James B. Kaler, Addison-Wesley, 1996
The Inflationary Universe - the quest for a new theory of cosmic origins. Alan Guth, Addison-Wesley, 1997
Principles of Physical Cosmology, P.J.E.Peebles, Princeton University Press, 1993
