Deformed phase space in a two dimensional minisuperspace model

TL;DR

This paper investigates how noncommutativity and deformed Heisenberg algebra influence the classical and quantum evolution of a two-dimensional minisuperspace cosmological model, revealing both similarities and differences with standard cases.

Contribution

It provides exact and approximate solutions for a minisuperspace model incorporating noncommutativity and deformed Heisenberg relations, advancing understanding of quantum cosmology.

Findings

Exact solutions in commutative and noncommutative cases

Approximate solutions with deformed Heisenberg relations

Comparison of solutions highlighting differences and similarities

Abstract

We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two dimensional minisuperspace cosmological model in classical and quantum regimes. The phase space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain some approximate analytical solutions for the corresponding classical and quantum cosmology in the presence of the deformed Heisenberg relations between the phase space variables, in the limit where the minisuperspace variables are small. These results are compared with the standard commutative and noncommutative cases and similarities and differences of these solutions are discussed.