  I study a model which describes the birth of the universe using a global
topological phase transition with a complex manifold where the time, $\tau$, is
considered as a complex variable. Before the big bang $\tau$ is a purely
imaginary variable so that the space can be considered as Euclidean. The phase
transition from a pre-inflation to inflation is examined by studying the
dynamical rotation of the time on the complex plane. Back-reaction effects are
exactly calculated using Relativistic Quantum Geometry.
