论文标题
非犯罪性，Saez-Ballester理论和动力学通货膨胀
Noncommutativity, Saez-Ballester theory and kinetic inflation
论文作者
论文摘要
本文介绍了扩展的Sáez-Ballester（SB）理论的非交通（NC）版本。具体而言，考虑到空间平坦的Friedmann-Lema \^ıtre-Robertson-Walker〜（flrw）度量，我们提出了共轭力动量之间的适当动力变形，并应用了汉密尔顿形式主义，获得了运动变形方程。在我们的模型中，NC参数在变形的泊松支架和NC SB宇宙学方程中线性出现。当零时，我们得到相应的交换对应物。 Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; （ii）在晚期，加速度为零。通过建立一个适当的动态框架，我们表明可以在模型的许多初始条件和参数中获得结果（i）和（ii）。最后，我们指出，在场方程的级别上，人们可能会发现我们的NC模型和Starobinsky通货膨胀模型之间的相似之处。
This paper presents a noncommutative (NC) version of an extended Sáez-Ballester (SB) theory. Concretely, considering the spatially flat Friedmann-Lema\^ıtre-Robertson-Walker~(FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.
