**B. The Expanding Universe**

In the mid-twenties, Edwin Hubble was observing a group of objects
known as spiral nebulae ^{(7)}
These nebulae contain a very important class of stars known as Cepheid
Variables. Because the Cepheids have a characteristic variation in
brightness [9],
Hubble could recognize these stars
at great distances and then compare their observed luminosity to
their known luminosity. This allowed him to compute the distance
to the stars, since luminosity is inversely proportional to the
square of the distance
[9]. The intrinsic, or
absolute, luminosity is calculated from simple models that have
been commensurate with observations of near Cepheids.

When Hubble compared the distance of the Cepheids to their velocities (computed by the redshift of their spectrum) he found a simple linear relationship,

where _{H} is the
velocity of the galaxy, *H* is the
so-called Hubble Constant, and
is the displacement of
the galaxy from the Earth. It will be shown later that the Hubble
constant is not actually a constant, but can be a function of time
depending on the chosen model. The standard notation is to adopt
*H*_{0} as the `current' observed Hubble parameter, whereas
*H = H(t)* is referred to as the Hubble constant. The current
accepted value of the Hubble parameter is,

The unit of length, Mpc, stands for Megaparsec
^{(8)}

Hubble's interpretation of his data was crucial in helping determine the correct model for the universe. Hubble had found that the galaxies, on average, were receding away from us at a velocity proportional to their distance from us (1). This suggests a homogeneous, isotropic, and expanding universe. By this finding, the choices of cosmological models became greatly restricted.

Perhaps it is worth mentioning that the above analysis by Hubble
is not quite as easily done as one might think. One factor that
must be considered in the calculation of the Hubble velocity field
(1) is the concept of peculiar velocity. This is
the name given to the motion of a galaxy, relative to the CRF, due
to its rotation and motion as influenced by the gravitational pull
of nearby clusters. This speed, *v*_{p}
± 500 km
s^{-1}, can be neglected at far distances where the
Hubble speed, *V*_{H} >> 500 km s^{-1}.
Thus, when Hubble conducted his survey most of the nebulae were
too near to rule out an effect by the peculiar velocity. As a
result, Hubble found *H*_{0}
500 km
s^{-1} Mpc, much greater than the value
obtained today from surveys of type Ia
supernovae ^{(9)}

^{7} It would later be found that most
of these nebula were in fact galaxies
[6].
Back.

^{8} 1 Mpc =
10^{6} parsecs
light years 3 x
10^{16} meters.

A parsec is the distance to an object that
has an angular parallax of 1° and a baseline of 1 A.U.
For more on Observational Astronomy see
[10].
Back.

^{9} Supernova Ia, like Cepheid Variables, have a
known `signature' and can therefore be used as `Standard Candles',
but unlike the Cepheids, supernovae are much more luminous and can
therefore be seen at much greater distance
[11].
Back.