On the origin of inflation

In this paper we discuss a space-time having the topology of S^{3}xR but with different smoothness structure. This space-time is not a global hyperbolic space-time. Especially we obtain a time line with a topology change of the space from the 3-sphere to a homology 3-sphere and back but without a topology-change of the space-time. Among the infinite possible smoothness structures of this space-time, we choose a homology 3-sphere with hyperbolic geometry admitting a homogenous metric. Then the topology change can be described by a time-dependent curvature parameter k changing from k=+1 to k=-1 and back. The solution of the Friedman equation for dust matter (p=0) after inserting this function shows an exponential growing which is typical for inflation. In contrast to other inflation models, this process stops after a finite time.