The semiclassical stochastic wave function of the Universe in the third quantization formalism

We will show, within the framework of a simple model of a closed homogeneous and isotropic Universe containing a lambda term and a set of massless scalar fields, how quantized solutions of the Wheeler-DeWitt equation describing the wave functions of this model acquire the features of a random classical field at large values of the scale factor. The unexpected connection of the obtained solution with the well-known proposal of Hartle and Hawking for the choice of the wave function of the Universe will also be discussed.