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We analyze the semiclassical polymer dynamics of the inhomogeneous Mixmastermodel by choosing the cubed scale factor as the discretized configurationalvariable, while the anisotropies remain pure Einsteinian variables. Such amodified theory of gravity should be regarded as the appropriate framework todescribe the behavior of quantum mean values, both in polymer quantum mechanicsand in Loop Quantum Cosmology. We first construct the generalized Kasnersolution, including a massless scalar field and a cosmological constant in thedynamics. They account for a quasi-isotropization, inflationary-like mechanism.The resulting scenario links a singularity-free Kasner-like regime with ahomogeneous and isotropic de Sitter phase. Subsequently, we investigate therole of the three-dimensional scalar curvature, demonstrating that a bounce ofthe point-universe against the potential walls can always occur within thepolymer framework, also in the presence of a scalar field. However, the absenceof the singularity implies that the curvature is bounded. Therefore, thepoint-universe undergoes an oscillatory regime until it oversteps the potentialwalls (if the Big Bounce is not reached before). After that, a final stableKasner-like regime will last all the way toward the Big Bounce. Thus, thepresent study demonstrates that, as soon as a discretization of the volume ofthe universe is performed, the generic cosmological solution is non-chaotic andfree from singularities. It is likely that the same result can be achieved alsoin the loop quantum cosmology approach.

Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe