We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general selfinteracting potential and a background spacetime with positively curved spatial sections. By means of a phase space analysis, we give the conditions under which an initially contracting phase can be followed by a bounce and an inflationary phase lasting long enough (i.e., at least 60-70 e-folds) to suppress spatial curvature in today's observable universe. We find that, quite generically, this realization requires some amount of fine-tuning of the initial conditions. We study the effect of this background evolution on scalar perturbations by propagating an initial power-law power spectrum through the contracting phase, the bounce and the inflationary phase. We find that it is drastically modified, both spectrally (k−mode mixing) and in amplitude. It also acquires, at leading order, an oscillatory component, which, once evolved through the radiation and matter dominated eras, happens to be compatible with observational data.

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The causal interpretation of quantum mechanics is applied to a homogeneous and isotropic quantum universe, whose matter content is composed by non interacting dust and radiation. For wave functions which are eigenstates of the total dust mass operator, we find some bouncing quantum universes which reachs the classical limit for scale factors much larger than its minimum size. However these wave functions do not have unitary evolution. For wave functions which are not eigenstates of the dust total mass operator but do have unitary evolution, we show that, for flat spatial sections, matter can be created as a quantum effect in such a way that the universe can undergo a transition from an exotic matter dominated era to a matter dominated one.