DISTANT GALAXIES AND COSMOLOGICAL MODELS
Edward J.
Barlow
Member of National Academy of
Engineering
Recipient of NASA Public Service Award
Previous member Report
Review Committee of the National Research Council
Retired Vice President,
Research & Development, Varian Associates

Model III and IIIa - Critical Mass Density
Next, let us take into
account the gravitational attraction of the mass in the universe which will act
to slow down the expansion. It is tempting to think that the mass density now
really is the critical density mentioned above. Remember the orbits of the
planets being perfect circles to the astronomers of the Middle ages? Consider
next a Model III with significant mass density, in fact with just the
critical density giving us a flat space and being the dividing line
between universes which expand forever (like Model II) and ones which stop and
collapse again. For this model, the equations of general relativity take simple
forms (and take the same form as Newtonian equations). This turns out to be a
model which has been much used by cosmologists in interpreting their
experimental results. It has an appeal, being the special case in which the mass
density is exactly the critical value right after the big bang and stays the
critical value always. This model is called the Einstein deSitter model after
its authors. In this model, R(t) is proportional to t2/3. The results
for this model are shown in Figure III for an
age of the universe, tr, of 15 billion years. Again, the curves are
shown for various galaxies and for the light packets reaching us now. Since the
galaxies are slowing down, their labeled velocities in Figure III are the
velocity now, vr. In addition, the proper distance D shown is
how far away from us now a light packet is which was emitted from us at time
te.

Many cosmologists use this Model III in reporting their results of
observations of very distant galaxies or supernovae. If, for example, the
redshift, z, of a very distant galaxy is measured as 5.34 ( recent paper using
this model)(5) the model would say that the object was
observed when the universe was a bit less than 1 billion years old.

For this model, since the galaxies are slowing down, the age of the universe
is not 1/H0 but 2/3H0. Thus, Figure IIIa shows
this model also for an age of the universe of 10 billion years to correspond
with the 15 billion years of Model II, both having the same value of
H0.

Figure IV
shows the four concepts of distance discussed above for this Model III. It can
be seen that, although at very low values of z the different distances are quite
close, they diverge rapidly for larger values of z. Thus, it is interesting to
know which concept of distance is being used in papers reporting
observations of distant galaxies.

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Ed Barlow -- All rights reserved.

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