Noncommutativity Effects in FRW Scalar Field Cosmology

TL;DR

This paper investigates how noncommutativity in phase space influences the evolution and quantum states of a scalar field in FRW cosmology, revealing that momentum noncommutativity enhances universe probability and solution tunability.

Contribution

It provides a comparative analysis of classical and quantum cosmological models with noncommutative phase space, highlighting the role of momentum noncommutativity in universe dynamics.

Findings

Momentum noncommutativity improves solution tuning at classical level.

Noncommutative parameters impose bounds on solutions and wave functions.

Noncommutativity increases the probability of certain universe states.

Abstract

We study effects of noncommutativity on the phase space generated by a non-minimal scalar field which is conformally coupled to the background curvature in an isotropic and homogeneous FRW cosmology. These effects are considered in two cases, when the potential of scalar field has zero and nonzero constant values. The investigation is carried out by means of a comparative detailed analysis of mathematical features of the evolution of universe and the most probable universe wave functions in classically commutative and noncommutative frames and quantum counterparts. The influence of noncommutativity is explored by the two noncommutative parameters of space and momentum sectors with a relative focus on the role of the noncommutative parameter of momentum sector. The solutions are presented with some of their numerical diagrams, in the commutative and noncommutative scenarios, and their properties are compared. We find that impose of noncommutativity in the momentum sector causes more ability in tuning time solutions of variables in classical level, and has more probable states of universe in quantum level. We also demonstrate that special solutions in classical and allowed wave functions in quantum models impose bounds on the values of noncommutative parameters.