It is customary to consider that the primordial anisotropies seen in the CMB data stem from quantum vacuum fluctuations of the inflaton field. Moreover, it is sometimes argued that the singularity preceding the inflation phase must have somehow been smoothed out by quantum mechanical effects of gravitation. Using a quantum trajectory formalism, I will discuss how to effectively implement a version of quantum cosmology that not only resolves the singularity but also may have some observable consequences.