The research activity of Dott. M.V.Battisti, in collaboration with Dr. G.Montani, is focus in main three directions:

I) The cosmological implications of an evolutionary quantum gravity
II) The quantization of cosmological model in the framework of the generalized uncertainty principle
III) The analysis of the semi-classical limit of the quantum Universe.

- I) The phenomenological and cosmological implications of an evolutionary reformulation of non-perturbative quantum gravity are analyzed. In particular, a Schodinger quantum dynamics for the gravitational field associated to a generic cosmological model is considered and the corresponding eigenvalue problem solved. Furthermore, when a Planckian cut-off is imposed in the theory, the spectrum is imitated by below. This way, it was showed that from a phenomenological point of view, an evolutionary quantum cosmology overlaps the Wheeler-DeWitt approach. Therefore such approach can be inferred as appropriate to describe early stages of the Universe without significant traces on the later evolution.

- II) The quantization of cosmological models by using a deformed Heisenberg algebra is studied. This approach leads to the implementation of a minimal length in the minisuperspace dynamics. Such a minimal length is nothing but the non vanishing uncertainty in the configuration variables coming out from the generalized uncertainty principle, which is reproduced by the modified algebra. In our works (on the FRW and the Taub models) we show how the classical singularity is probabilistic suppressed and how the Universe approaches stationary states toward the Planckian region. Moreover, the Taub GUP wave packets exhibit a right behavior in predicting a quasi-isotropic configuration for the Universe.

- III) Starting from the intuition of Vilenkin about an (only possible) approximative interpretation of the Universe wave function, the quasi-classical limit of the Universe is analyzed. In particular, the idea that the isotropic volume of the Universe has, in some sense, a privileged role in this process is performed. However, this is only a work in progress and therefore without precise results.