Asymptotically equivalent functions and ultrafilters applied to noncommutative quantum cosmology

Abstract

Using the semi-classical approximation to the Wheeler-DeWitt equation obtained via Arnowitt-Deser-Misner (ADM) formalism in the Friedmann-Lemaître-Robertson-Walker (FLRW) model coupled to a scalar field and positive cosmological constant, and in the Kantowski-Sachs (KS) Universe, we introduced a deformation on the commutation relation for the minisuperspace variables and find an explicit semiclassical expression equivalent, in an adequate limit, to the solution with the aid of asymptotically equal functions and the theory of Ultrafilters, offering a suggestive alternative to sketch the behavior of the dynamical system involved without the need to solve it numerically.