arXiv 1701.011622017-01-04gr-qc

幻影流体存在下的非对易宇宙学模型

Noncommutative cosmological model in the presence of a phantom fluid

G. Oliveira-Neto, A. R. Vaz

备注：: 27 pages and 9 figures

摘要：

研究了非对易经典Friedmann-Robertson-Walker宇宙学模型。空间部分的恒定曲率可以是正的（$k=1$）、负的（$k=-1$）或零（$k=0$）。该物质由具有负压的理想流体（体模流体）表示，其满足状态方程$p =αρ$，具有$α< - 1$，其中$p$是压力，$ρ$是能量密度。我们使用舒茨的形式主义，以书面完美的流体哈密顿量。非交换性是由非平凡的泊松括号之间的几个变量的模型。为了恢复的描述中的交换变量，我们引入依赖于一个非交换参数（$γ$）的变量变换。引入非对易性的主要动机是试图解释目前宇宙的加速膨胀。我们得到这些模型的动力学方程，并解决它们。解具有四个常数：$γ$，与流体能量$C$、$k$、$α$和模型变量的初始条件相关联的参数。对于$α$的每个值，我们得到不同的运动方程。然后，我们比较了目前的非对易模型和相应的对易模型（$γ\to 0$）之间的宇宙演化。结果表明，$γ$对描述加速宇宙是非常有用的.我们估计$γ$的价值，为目前的宇宙条件。然后，利用这个$γ$的值，在一个非对易宇宙学模型中，我们计算这个宇宙到达{ \it大裂缝}所需的时间。

英文摘要：

We study noncommutative classical Friedmann-Robertson-Walker cosmological models. The constant curvature of the spatial sections can be positive ($k=1$), negative ($k=-1$) or zero ($k=0$). The matter is represented by a perfect fluid with negative pressure, phantom fluid, which satisfies the equation of state $p =αρ$ , with $α< - 1$, where $p$ is the pressure and $ρ$ is the energy density. We use Schutz's formalism in order to write the perfect fluid Hamiltonian. The noncommutativity is introduced by nontrivial Poisson brackets between few variables of the models. In order to recover a description in terms of commutative variables, we introduce variables transformations that depend on a noncommutative parameter ($γ$). The main motivation for the introduction of the noncommutativity is trying to explain the present accelerated expansion of the universe. We obtain the dynamical equations for these models and solve them. The solutions have four constants: $γ$, a parameter associated with the fluid energy $C$, $k$, $α$ and the initial conditions of the models variables. For each value of $α$, we obtain different equations of motion. Then, we compare the evolution of the universe between the present noncommutative models and the corresponding commutative ones ($γ\to 0$). The results show that $γ$ is very useful for describing an accelerating universe. We estimate the value of $γ$, for the present conditions of the Universe. Then, using that value of $γ$, in one of the noncommutative cosmological models, we compute the amount of time this universe would take to reach the {\it big rip}.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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