*3. The Open Model*

The so-called Open Model ^{(13)}
is the case where *k* = -1
and the geometry is said to be hyperbolic. Taking *k* = -1 in the
Friedmann equations (29), (28),

Solving these equations
(39), (40) yields the same value
of the density (37) as the closed model, but in this
case *q* < 1/2 and
< 1, as previously discussed.

^{13} Although it is a standard practice to
refer to this case
(*k* = -1) as the `Open' Model, it should be noted that the model
can actually correspond to a closed universe. This is the result
of a non-trivial topology, which results in geometry that can be
hyperbolic; but, the topology can cause it to be contained in a
finite space [16,
17].