Hořava–Lifshitz cosmological models with noncommutative phase space variables

• Published in: General relativity and gravitation 2019-07, Vol.51 (7), p.1-27, Article 95
• Main Authors: Abreu, E. M. C., Mendes, A. C. R., Oliveira-Neto, G., Neto, J. Ananias, Rodrigues, L. G. Rezende, de Oliveira, M. Silva
• Format: Article
• Language: English
• Subjects: Astronomical models; Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Cosmology; Curvature; Differential Geometry; Gravitation theory; Gravity; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Research Article; Theoretical; Universe
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-019-2577-3

In this work, we will analyze a noncommutative (NC) phase space version of the Friedmann–Robert–Walker cosmological models within the gravitational Hořava–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, phase space 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.