D. Matter Dominated Models
The present epoch is
best described by a matter dominated universe, so it is perhaps
best to explore this model first. Again, matter domination
corresponds to a non-relativistic, homogeneous, isotropic `dust'
filled universe with zero pressure. By setting p = 0 in (15)
and incorporating the 
term
into a total density,
T =
+
/ (8
G), the Friedmann equations
for a matter dominated universe emerge,
Again, the value of k describes the geometry of the
space. Equation (29) is actually obtained by
combining (14) and (15) and is often called the
acceleration equation.
The idea of the total density,
T, might be a bit
confusing since it has been stated that the model is matter
dominated. Although this is true, there can still be a small
contribution in the form of radiation and other forms of energy,
such as dark matter. The point is that any of these should be much
less than M
for the model to be accurate. It will also be
seen that M
can also be broken into different
contributions as tacitly stated in the previous remark about dark
matter. For the remainder of this section we take
to mean
T to keep
the notation as simple as possible.