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**1.8 Expansion of the Universe**

We now come to the observations that Launched modern cosmology. Between 1912 and 1925, V.M. Slipher measured the shifts in the spectra of more than 20 objects that later turned out to be galaxies. Slipher was surprised that all shifts were towards the red end. Later, E. Hubble and M. Humason extended Slipher's list of observations to more galaxies and to the brightest cluster galaxies. An example of the pattern that emerged when the redshift was plotted against distance of a galaxy is shown in Figure 1.21 (see also Figure 1.22).

If all galaxies seen are equally bright, then the magnitudes are proportional to the logarithm of distances. Thus the straight line drawn through the cluster of points corresponds to the linear relation

where *D*
is the distance of the galaxy and *z* its redshift. If the redshift were
due to the Doppler effect, then we could ascribe to the galaxy a
velocity of recession *V* relative to us. (Since *z* << 1 in
the observations of Hubble and Humason, and the Newtonian Doppler shift
formula is valid.) The constant *H*_{0} is now known as
*Hubble's constant*.

If instead of plotting *z* against the distance *D*, log
*z* is plotted
against the apparent magnitude *m* of the galaxy, then another
straight-line relation shows up (see section 3.6 for a definition of
apparent magnitude).

For,

and (1.3) implies

Since the distances of remote galaxies are determined through their apparent magnitudes (as discussed in Chapter 9), (1.5) is the practical form of Hubble's linear relation (1.3).

The relation (1.3) is called *Hubble's law*. It was published as a
linear law by Hubble in 1929, and it caused great excitement. For the
prima facie interpretation of Hubble's law seemed to be that there was a
great explosion in our neighbourhood of the universe from which galaxies
were thrown out. However, the linearity of Hubble's law shows that we
need not consider ourselves in any special position in the universe. If
we viewed the population of galaxies from any other galaxy, we would
notice the same Hubble's law. The combination of this fact with the
homogeneity and isotropy of the distribution of the population of
galaxies suggests a highly regular structure of the universe.

Imagine a piece of dough with self-raising flour being baked in the oven, and suppose we have spread caraway seeds uniformly throughout the dough. As the dough bakes it expands, and the seeds move away from each other. The phenomenon of the recession of galaxies might be looked upon in the same light. They are points embedded in space that is expanding. This notion of galaxies embedded in expanding space led to the concept of the expanding universe.

The rate of expansion is characterized by Hubble's constant. Hubble
obtained a value for *H*_{0} in the neighbourhood of 530 km
s^{-1} Mpc^{-1}. (Note
that these units arise because *H*_{0} is velocity divided
by distance. The dimensions of *H*_{0}^{-1} are
simply those of time.) As we will discuss in
section 9.2, Hubble had grossly underestimated the galactic distances,
with the result that his value of *H*_{0} was too high. The
value of *H*_{0} is
now believed to lie in the range of 50 to 100 km s^{-1}
Mpc^{-1}. We will
write it as 100 *h*_{0} km s^{-1} Mpc^{-1},
where *h*_{0} lies between 0.5 and 1. Notice
that if we assume Hubble's law we can estimate the distance of an
extragalactic object from its redshift.