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arXiv 1804.03633gr-qc
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形变相空间中的暴胀宇宙

Inflationary Universe in Deformed Phase Space Scenario

S. M. M. Rasouli, N. Saba, M. Farhoudi, J. Marto, P. Moniz

摘要:

考虑一个均匀标量场与引力最小耦合的非对易暴胀模型。特定的NC通货膨胀设置产生了全新的后果。我们首先分析了自由场的情况下,随后检查的情况下,标量场受到多项式和指数势。我们建议使用动量之间的正则变形,在空间平坦的FLRW宇宙,而弗里德曼方程保持不受影响的弗里德曼加速度方程(从而克莱因-戈登方程)被修改的额外的长期线性NC参数。动量的这种具体的非对易性允许其他NC模型似乎不允许的有趣的动力学。让我们说得更确切些。这个额外的项表现为唯一明确的压力,在适当的情况下意味着宇宙加速膨胀的时期。我们发现,在标量场潜力的情况下,与交换的情况下,其中的标度因子总是减速,我们得到的NC参数的小负值的暴胀阶段。随后,一个适当的减速阶段,提供了一个有趣的模型,在通货膨胀模型的优雅退出问题的加速膨胀期间顺利取代。此外,在自由标量场的情况下,我们证明了不仅视界问题得到了解决,而且我们模型的标度因子演化方程与$R^2$(Starobinsky)暴胀模型的标度因子演化方程有某些相似之处.因此,我们的NC模型不仅可以作为一个成功的动力学暴胀的合适方案,而且也是一个方便的设置,以获得标量场势存在时具有优雅出口的暴胀宇宙。

英文摘要:

We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting produces entirely new consequences. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat FLRW universe, and while the Friedmann equation remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the $R^2$ (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.

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