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 nonzero transition probability. The transition may be interpreted as a spatial reflection of the wave function in minisuperspace.