非对易性、Saez-Ballester理论与动力学暴胀
Noncommutativity, Saez-Ballester theory and kinetic inflation
摘要：
本文提出了一个扩展的Sáez-Ballester（SB）理论的非对易（NC）版本。具体地说，考虑空间平坦的Friedmann-Lemitre-Robertson-Walker~（FLRW）度规，在共轭动量之间提出了一种适当的动力学变形，并应用Hamilton形式，得到了变形后的运动方程.在我们的模型中，NC参数线性地出现在变形泊松括号和NC SB宇宙学方程中。当它为零时，我们得到相应的交换对应物。即使把我们的注意力限制在一个特殊的情况下，既没有普通物质，也没有标量势，我们表明，非对易性的影响提供了有趣的结果：应用数值努力非常小的值的NC参数，我们表明：（i）在宇宙的早期，有一个膨胀阶段与一个优雅的出口，为相关的名义条件得到满足;（ii）对于后期，存在零加速时期。通过建立一个适当的动力学框架，我们表明，结果（i）和（ii）可以得到许多组的初始条件和模型的参数。最后，我们指出，在场方程的水平上，人们可能会发现我们的NC模型和Starobinsky暴胀模型之间的密切相似之处。
英文摘要：
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.
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