Asymptotically Equivalent Functions and Ultrafilters applied to Noncommutative Quantum Cosmology

TL;DR

This paper employs asymptotically equivalent functions and ultrafilter theory to analyze semiclassical solutions of quantum cosmological models, providing an alternative to numerical solutions in the Wheeler-DeWitt framework.

Contribution

It introduces a novel application of ultrafilter theory and asymptotically equivalent functions to approximate solutions in noncommutative quantum cosmology.

Findings

Explicit semiclassical expressions derived

Alternative to numerical solutions proposed

Deformation of commutation relations analyzed

Abstract

Using the semi-classical approximation to the Wheeler-DeWitt equation obtained via Arnowitt-Deser-Misner (ADM) formalism in the Friedmann-Lemaitre-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.