arXiv subjects

M. Silva de Oliveira

Publications and source records attributed to M. Silva de Oliveira.

3 recordsLinked to original sources

arXiv2018

Hořava-Lifshitz cosmological models in noncommutative space-times

In this work, we will analyze a noncommutative (NC) 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, 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.

gr-qc↗

arXiv2016

Noncommutativity in the early Universe

In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter $β$. We compute the scale factor expected value ($\left $) for several values of $β$. For all of them, $\left $ oscillates between maxima and minima values and never vanishes. It gives an initial indication that those models are free from singularities, at the quantum level. We improve this result by showing that if we subtract a quantity proportional to the standard deviation of $a$ from $\left $, this quantity is still positive. The $\left $ behavior, for the present model, is a drastic modification of the $\left $ behavior in the corresponding commutative version of the present model. There, $\left $ grows without limits with the time variable. Therefore, if the present model may represent the early stages of the Universe, the results of the present paper give an indication that $\left $ may have been, initially, bounded due to noncommutativity. We also compute the Bohmian trajectories for $a$, which are in accordance with $\left $, and the quantum potential $Q$. From $Q$, we may understand why that model is free from singularities, at the quantum level.

gr-qc↗

arXiv2016

Can noncommutativity affect the whole history of the Universe?

We study a classical, noncommutative (NC), Friedmann-Robertson-Walker cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial noncommutativity between some canonical variables is rewritten, such that, we end up with commutative variables and a NC parameter. Initially, we derive the scale factor dynamic equations for the general situation, without specifying the perfect fluid or the curvature of the spatial sections. Next, we consider two concrete situations: a radiation perfect fluid and dust. We study all possible scale factor behaviors, for both cases. We compare them with the corresponding commutative cases and one with the other. We obtain, some cases, where the NC model predicts a scale factor expansion which may describe the present expansion of our Universe. Those cases are not present in the corresponding commutative models. Finally, we compare our model with another NC model, where the noncommutativity is between different canonical variables. We show that, in general, it leads to a scale factor behavior that is different from our model.

gr-qc↗