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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),

Equation 39 (39)

Equation 40 (40)

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 Omega < 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].