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.