  In this paper, we analyze the dynamics of an isotropic closed Universe in the
presence of a cosmological constant term and we compare its behavior in the
standard Wheeler-DeWitt equation approach with the one when a Lagrangian fluid
is considered in the spirit of the Kuchar-Brown paradigm. In particular, we
compare the tunnelling of the Universe from the classically forbidden region to
the allowed one, showing that considering a time evolution deeply influences
the nature of the model. In fact, we show that in the presence of the
Lagrangian fluid, the cosmological singularity is restored both in the
classical and the quantum regime. However, in the quantum regime the
singularity is probabilistically suppressed for some energy eigenvalues and in
the case the latter is equal to zero, one recovers the standard WDW case.
Finally, we introduce a cut-off physics feature in the Minisuperspace by
considering a Polymer quantum mechanical approach, mainly limiting our
attention to the semi-classical dynamics (the quantum treatment is inhibited by
the non-local nature of the Hamiltonian operator). We show that the singularity
is again removed, like in the fluid-free model, and a bouncing cosmology
emerges so that the present model could mimic a cyclic cosmology.
