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Non-minimally coupled Einstein Gauss Bonnet inflation phenomenology in view of GW170817
Annals of Physics ( IF 3 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.aop.2020.168250
S.D. Odintsov , V.K. Oikonomou , F.P. Fronimos

We study the inflationary phenomenology of a non-minimally coupled Einstein Gauss-Bonnet gravity theory, in the presence of a scalar potential, under the condition that the gravitational wave speed of the primordial gravitational waves is equal to unity, that is $c_T^2=1$, in natural units. The equations of motion, which are derived directly from the gravitational action, form a system of differential equations with respect to Hubble's parameter and the inflaton field which are very complicated and cannot be solved analytically, even in the minimal coupling case. In this paper, we present a variety of different approximations which could be used, along with the constraint $c_T^2=1$, in order to produce an inflationary phenomenology compatible with recent observations. All the different approaches are able to lead to viable results if the model coupling functions obey simple relations, however, different approaches contain different approximations which must be obeyed during the first horizon crossing, in order for the model to be rendered correct. Models which may lead to a non-viable phenomenology are presented as well in order to understand better the inner framework of this theory. Furthermore, since the velocity of the gravitational waves is set equal to $c_T^2=1$, as stated by the striking event of GW170817 recently, the non-minimal coupling function, the Gauss-Bonnet scalar coupling and the scalar potential are related to each other. Here, we shall assume no particular form of the scalar potential and we choose freely the scalar functions coupled to the Ricci scalar and the Gauss-Bonnet invariant. Certain models are also studied in order to assess the phenomenological validity of the theory, but we need to note that all approximations must hold true in order for a particular model to be valid.

中文翻译:

鉴于GW170817的非最小耦合Einstein Gauss Bonnet暴胀现象学

我们研究了非最小耦合爱因斯坦高斯-博内引力理论的暴胀现象学,在标量势的存在下,在原始引力波的引力波速度等于1的条件下,即$c_T^2 =1$,自然单位。运动方程直接从引力作用推导出来,形成了一个关于哈勃参数和暴胀子场的微分方程系统,这些方程非常复杂,即使在最小耦合情况下也无法解析求解。在本文中,我们提出了各种可以使用的不同近似值,以及约束 $c_T^2=1$,以产生与最近的观察结果兼容的暴胀现象学。如果模型耦合函数服从简单的关系,那么所有不同的方法都能够产生可行的结果,但是,不同的方法包含不同的近似值,在第一次穿越时必须遵守这些近似值,以便正确地渲染模型。为了更好地理解该理论的内部框架,还提供了可能导致不可行现象学的模型。此外,由于引力波的速度被设置为等于 $c_T^2=1$,正如最近 GW170817 的撞击事件所述,非最小耦合函数、Gauss-Bonnet 标量耦合和标量势是相关的对彼此。在这里,我们不假设标量势的特定形式,我们自由选择耦合到 Ricci 标量和 Gauss-Bonnet 不变量的标量函数。
更新日期:2020-09-01
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