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We compare in some detail Polymer Quantum Mechanics and the GeneralizedUncertainty Principle approach to clarify to what extent we can treat them onthe same footing. We show that, while on a semiclassical level they may beformulated as similar modifications of the Poisson algebra, on a quantum levelthey intrinsically differ because PQM implies no absolute minimal uncertaintyon position. Then we implement these schemes to Bianchi I cosmology on asemiclassical level deforming only the algebra of the Universe volume,searching for alternative formulations able to account for the modifiedFriedmann equations emerging in Brane Cosmology and Loop Quantum Cosmology. Ona pure quantum level, we implement the two approaches through their originalsetups and reduce the two resulting Wheeler-DeWitt equations to the samemorphological structure, showing how the polymer formalism is associated with abouncing dynamics while in the Generalized Uncertainty Principle case thesingularity is still present. The implications of the wavepacket spreading arealso discussed in both approaches, outlining that, when the singularitysurvives, the Planckian era must necessarily be approached by a fully quantum(non-peaked) state of the Universe.

Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms