Scalar field fluctuations in Pre-Big-Bang Cosmologies

Jordan-Brans-Dicke theories with a linearized potential for the scalar field are investigated in the framework of the stochastic approach. The fluctuations of this field are examined and their backreaction on the classical background is described. We compute the mode functions and analyze the time evolution of the variance of the stochastic ensemble corresponding to the full quantum scalar field in the pre-big-bang regime. We compute fluctuations of the term discriminating between the two branches of solutions present in the theory. We find, both analytically and upon direct integration of the stochastic equations of motion, that the dispersion of these fluctuations grows to achieve the magnitude of the term separating the two classical solutions. This means that the ensembles representing classical solutions which belong to different branches do overlap; this may provide a quantum mechanical realization at the level of field theory to change among solutions belonging to different branches.