In this paper, we will show that a power law asymptotic de Sitter inflation will be established for all values of Hankel indices ν that relate to the different background spacetimes of the universe in their evolution. First, we calculate the relations for the Hubble, deceleration, slow roll and the equation of state parameters in terms of the Hankel function index ν. We then show that the obtained relations and figures correspond to the conventional limit conditions for pure de Sitter inflation. As an important result, power law quasi-de Sitter inflation is more likely to occur after exponential pure de Sitter inflation. Also, in the proposed model, the universe can always be in the accelerating expansion phase for all values of index ν.

中文翻译：

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不同几何背景下的渐近德西特膨胀

在本文中，我们将证明对于 Hankel 指数的所有值都将建立幂律渐近德西特膨胀ν这与宇宙演化过程中不同的背景时空有关。首先，我们根据汉克尔函数指数计算哈勃、减速、慢滚和状态参数方程的关系ν. 然后我们表明，获得的关系和数字对应于纯德西特暴胀的常规极限条件。作为一个重要结果，幂律准德西特暴胀更可能发生在指数纯德西特暴胀之后。此外，在所提出的模型中，对于所有指数值，宇宙总是处于加速膨胀阶段ν.