Inflationary and Deflationary Branches in Extended Pre--Big Bang Cosmology

The pre--big bang cosmological scenario is studied within the context of the Brans--Dicke theory of gravity. An epoch of superinflationary expansion may occur in the pre--big bang phase of the Universe's history in a certain region of parameter space. Two models are considered that contain a cosmological constant in the gravitational and matter sectors of the theory, respectively. Classical pre-- and post--big bang solutions are found for both models. The existence of a curvature singularity forbids a classical transition between the two branches. On the other hand, a quantum cosmological approach based on the tunneling boundary condition results in a non--zero transition probability. The transition may be interpreted as a spatial reflection of the wavefunction in minisuperspace.