Notes on Relativity and Cosmology - Physics Department, UCSB

296 CHAPTER 10. COSMOLOGY
10.4 Observations and Measurements
So, which is the case for our universe? How can we tell? Well, one way to figure
this out is to try to measure how fast the universe was expanding at various
times in the distant past. This is actually not as hard as you might think: you
see, it is very easy to look far backward in time. All we have to do is to look
at things that are very far away. Since the light from such objects takes such a
very long time to reach us, this is effectively looking far back in time.
10.4.1 Runaway Universe?
The natural thing to do is to try to enlarge on what Hubble did. If we could
figure out how fast the really distant galaxies are moving away from us, this will
tell us what the Hubble constant was like long ago, when the light now reaching
us from those galaxies was emitted. The redshift of a distant galaxy is a sort
of average of the Hubble constant over the time during which the signal was in
transit, but with enough care this can be decoded to tell us about the Hubble
constant long ago. By measuring the rate of decrease of the Hubble constant,
we can learn what kind of universe we live in.
However, it turns out that accurately measuring the distance to the distant
galaxies is quite difficult. (In contrast, measuring the redshift is easy.) Until
recently, no one had seriously tried to measure such distances with the accuracy
that we need. However, a few years ago it was realized that there may be a
good way to do it using supernovae.
The particular sort of supernova of interest here is called ‘Type Ia.’ Astrophysicists
believe that type Ia supernovae occur when we have a binary star system
containing one normal star and one white dwarf. We can have matter flowing
from the normal star to the white dwarf in an accretion disk, much as matter
would flow to a neutron star or black hole in that binary star system. But
remember that a white dwarf can only exist if the mass is less than 1.4 solar
masses. When extra matter is added, bringing the mass above this threshold,
the electrons in the core of the star get squeezed so tightly by the high pressure
that they bond with protons and become neutrons. This releases vast amount
of energy in the form of neutrinos (another kind of tiny particle) and heat which
results in a massive explosion: a (type Ia) supernova.
Anyway, it appears that this particular kind of supernova is pretty much always
the same. It is the result of a relatively slow process where matter is gradually
added to the white dwarf, and it always explodes when the total mass hits
1.4 solar masses. In particular, all of these supernovae are roughly the same
brightness (up to one parameter that astrophysicists think they know how to
correct for). As a result, supernovae are a useful tool for measuring the distance
to far away galaxies. All we have to do is to watch a galaxy until one of these
supernovae happens, and then see how bright the supernova appears to be.
Since it’s actual brightness is known, we can then figure out how far away it