Late time acceleration in a non-commutative model of modified cosmology

TL;DR

This paper explores how noncommutativity in phase space affects modified cosmological models, leading to potential explanations for late-time cosmic acceleration through exact solutions in both commutative and noncommutative frameworks.

Contribution

It introduces a noncommutative phase space approach to modified cosmology and derives exact solutions comparing commutative and noncommutative cases.

Findings

Noncommutativity induces a deformed product law in phase space.

Exact solutions show differences in cosmic evolution due to noncommutativity.

Noncommutative effects can explain late-time acceleration in the universe.

Abstract

We investigate the effects of noncommutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such noncommutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an $\alpha$-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.