  We discuss a spacetime having the topology of $S^{3}\times\mathbb{R}$ but
with a different smoothness structure. The initial state of the cosmos in our
model is identified with a wildly embedded 3-sphere (or a fractal space). In
previous work we showed that a wild embedding is obtained by a quantization of
a usual (or tame) embedding. Then a wild embedding can be identified with a
(geometrical) quantum state. During a decoherence process this wild 3-sphere is
changed to a homology 3-sphere. We are able to calculate the decoherence time
for this process. After the formation of the homology 3-sphere, we obtain a
spacetime with an accelerated expansion enforced by a cosmological constant.
The calculation of this cosmological constant gives a qualitative agreement
with the current measured value.
