Notes on Relativity and Cosmology - Physics Department, UCSB

304 CHAPTER 10. COSMOLOGY
clumped together. If we look at how fast the galaxies in a given clump orbit
each other, we again find a bit more mass than we expected.
It turns out that something like 90% of the matter out there is stuff that we
can’t see. For this reason, it is called ‘Dark Matter.’ Interestingly, although
it is attached to the galaxies, it is spread a bit more thinly than is the visible
matter. This means that a galaxy is surrounded by a cloud of dark matter
than is a good bit larger than the part of the galaxy that we can see. All of
these measurements of gravitational effects bring the matter count up to about
Ω matter = .4.
Now, there is of course a natural question: Just what is this Dark Matter stuff
anyway? Well, there are lots of things that it is not. For example, it is not
a bunch of small black holes or a bunch of little planet-like objects running
around. At least, the vast majority is not of that sort. That possibility has
been ruled out by studies of gravitational lensing (a subject on which I wish
I had more time to spend). Briefly, recall that general relativity predicts that
light ‘falls’ in a gravitational field and, as a result, light rays are bent toward
massive objects. This means that massive objects actually act like lenses, and
focus the light from objects shining behind them. When such a ‘gravitational
lens’ passes in front of a star, the star appears to get brighter. When the lens
moves away, the star returns to its original brightness. By looking at a large
number of stars and seeing how often they happen to brighten in this way,
astronomers can ‘count’ the number of gravitational lenses out there. To make
a long story short, there are too few such events for all of the dark matter to
be clumped together in black holes or small planets. Instead, most of it must
be spread out more evenly.
Even more interestingly, it cannot be just thin gas..... That is, there are strong
arguments why the dark matter, whatever it is, cannot be made up of protons
and neutrons like normal matter! To understand this, we need to continue
the story of the early universe as a movie that we run backward in time. We
discussed earlier how there was a very early time (just before decoupling) when
the Universe was so hot and dense that the electrons were detached from the
protons. Well, continuing to watch the movie backwards the universe becomes
even more hot and dense. Eventually, it becomes so hot and dense that the
nuclei fall apart.
Now there are just a bunch of free neutrons and protons running around, very
evenly spread throughout the universe. It turns out that we can calculate what
should happen in such a system as the universe expands and cools. As a result,
one can calculate how many of these neutrons and protons should stick together
and form Helium vs. how many extra protons should remain as Hydrogen. This
process is called ‘nucleosynthesis.’ One can also work out the proportions of
other light elements like Lithium.... (The heavy elements were not made in
the big bang itself, but were manufactured in stars and supernovae.) To cut
short another long story, the more dense the stuff was, the more things stick
together and the more Helium and Lithium should be around. Astronomers are
pretty good at measuring the relative abundance of Hydrogen and Helium, and