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arXiv 2108.06218gr-qc
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圈量子宇宙学中Hilltop势预暴胀的初始条件

Initial conditions of pre-inflation with Hilltop potential in loop quantum cosmology

M. Shahalam, Kuralay Yesmakhanova, Zhanar Umurzakhova

摘要:

本文在圈量子宇宙学框架下研究了Hilltop势作用下的预暴胀动力学。将暴胀子场在量子反弹时的初始条件分为两类,一类是以动能为主的初始条件,另一类是以势能为主的初始条件。在这两种情况下,物理上可行的初始值的暴胀子场在反弹的数值,产生所需的慢滚暴胀,也足够数量的$e$折叠。为与观察结果一致,至少需要60倍$e$。在初始条件为动能主导的情况下,本底的数值演化分为三个不同的区域:{ \it反弹、过渡和慢卷暴胀},而在势能主导的情况下,反弹和过渡相消失,但仍实现了慢卷暴胀。这在Hilltop电位的$p=4$和$v=1 M_{Pl}$的情况下是正确的。然而,对于其他情况下,慢卷膨胀不能得到。此外,我们还研究了Hilltop势的相空间分析,讨论了在所选参数下的相空间轨迹。

英文摘要:

In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of $e$-folds. To be consistent with observations at least 60 $e$-folds are required. In case of kinetic energy dominated initial conditions of inflaton field at the bounce, the numerical evolution of the background prior to preheating is divided into three different regions: {\it bouncing, transition and slow-roll inflation} whereas bouncing and transition phases disappear in the potential energy dominated case but still slow-roll inflation is achieved. This is true in case of $p=4$ and $v=1 M_{Pl}$ of Hilltop potential. However for other cases, slow-roll inflation can not be obtained. Moreover, we study the phase space analysis for Hilltop potential and discuss the phase space trajectories under the chosen parameters.

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