Ho\v{r}ava-Lifshitz cosmological models in noncommutative space-times

TL;DR

This paper explores noncommutative versions of Hořava-Lifshitz cosmological models, revealing new dynamics and potential explanations for accelerated universe expansion through modified classical equations.

Contribution

It introduces a noncommutative framework into Hořava-Lifshitz cosmology using Faddeev-Jackiw formalism, uncovering novel behaviors and accelerated expansion scenarios.

Findings

Noncommutative models exhibit new dynamics compared to commutative ones.

Some models predict accelerated expansion of the universe.

Results depend on matter type and spatial curvature.

Abstract

In this work, we will analyze a noncommutative (NC) version of the Friedmann-Robert-Walker cosmological models within the gravitational Ho\v{r}ava-Lifshitz theory. The matter content of the models is described by a perfect fluid and the constant curvature of the spatial sections may be positive, negative or zero. In order to obtain this theory, we will use the Faddeev-Jackiw symplectic formalism to introduce, naturally, space-time noncommutativity inside the equations that provide the dynamics of the theory. We will investigate, in details, the classical field equations of a particular version of the NC models. The equations will be modified, with respect to the commutative ones, by the introduction of a NC parameter. We will demonstrate that various NC models, with different types of matter and spatial constant curvatures, show several interesting and new results relative to the corresponding commutative ones. We will pay special attention to some cases, where the NC model predicts a scale factor accelerated expansion, which may describe the current state of our Universe.