标题： 进一步完善仿射f(G)引力中的景观dS猜想 显示英文标题

标题： Further Refining Swampland dS Conjecture in Mimetic f(G) Gravity

摘要： 模仿引力分析已被研究作为一种在各种广义相对论扩展理论中的理论，例如模仿f(R)引力、模仿f(R, T)引力、模仿f(R, G)引力等，在文献中。 本文提出了一组由模仿条件产生的方程，并结合模仿f(G)引力和低地dS猜想研究宇宙暴胀。 我们分析并评估这些结果。 因此，我们首先全面介绍模仿f(G)引力，并计算一些宇宙学参数，如标量谱指数、张量-标量比和慢滚参数。 同时，我们根据模仿f(G)引力研究势能。 然后我们将用这种条件挑战低地dS猜想。 通过将低地dS猜想的系数即 $C_{1}$ 和 $C_2$ 表示为 $n_{s}$ 和 $r$ 的函数，我们绘制了一些图表，并确定了这些宇宙学参数和这些系数的允许范围，最后，将这些结果与观测数据如普朗克和BICEP2/Keck阵列数据进行比较。 我们表明 $C_{1}$ 和 $C_2$ 不是 $\mathcal{O}(1)$，因此对于这个暴胀模型，改进的低地dS猜想不成立。 然后我们进一步用修正的悬崖地 conjecture 对其进行检验，该 conjecture 有一系列自由参数，如$a,b>0$，$q>2$，以及$a+b=1$。 通过调整这些参数，可以讨论该 conjecture 与暴胀模型的相容性。 我们确定修正的悬崖地 conjecture 是满足的。 当$a < \frac{1}{1.00489}=0.99513$时，我们可以总是找到$a$、$b$和$q$，它们的值大于 2，即对于$q=2.4$，我们找到$0.99185\leq a < 1$，我们可以根据条件$a < 0.99513$选择$a=0.99235$。 我们也知道$b=1-a$，因此我们将得到$1-0.99235=0.00765 > 0$。 显示英文摘要

摘要： Mimetic gravity analysis has been studied as a theory in various types of general relativity extensions, such as mimetic f(R) gravity, mimetic f(R, T) gravity, mimetic f(R, G) gravity, etc., in the literature. This paper presents a set of equations arising from mimetic conditions and studies cosmic inflation with a combination of mimetic f(G) gravity and swampland dS conjectures. We analyze and evaluate these results. Therefore, we first thoroughly introduce the mimetic f(G) gravity and calculate some cosmological parameters such as the scalar spectral index, the tensor-to-scalar ratio, and the slow-roll parameters. Also, we investigate the potential according to the mimetic f(G) gravity. Then we will challenge the swampland dS conjectures with this condition. By expressing the coefficient of swampland dS conjectures viz $C_{1}$ and $C_2$ in terms of $n_{s}$ and $r$, we plot some figures and determine the allowable range for each of these cosmological parameters and these coefficients, and finally, compare these results with observable data such as Planck and BICEP2/Keck array data. We show $C_{1}$ and $C_2$ are not $\mathcal{O}(1)$, so the refining swampland dS conjecture is not satisfied for this inflationary model. Then we examine it with further refining swampland dS conjecture, which has a series of free parameters such as $a,b>0$, $q>2$, and $a+b=1$. By adjusting these parameters, the compatibility of the mentioned conjecture with the inflationary model can be discussed. We determine the further refining swampland dS conjecture is satisfied. when $a < \frac{1}{1.00489}=0.99513$, we can always find $a$, $b$ and $q$ whose value is larger than 2, viz for $q=2.4$, we find $0.99185\leq a < 1$, which we can choose $a=0.99235$ according to the condition $a < 0.99513$. Also we know $b=1-a$, so we will have $1-0.99235=0.00765 > 0$.