标题： 一种适用于 Bianchi-I 宇宙学的通用动力系统公式，其中包含在$f(Q)$引力中的各向同性流体 显示英文标题

标题： A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity

摘要： 在本文中，我们提出了一个通用的动力系统公式，用于在共存规范连接分支以及$f(Q)$引力理论的一个非共存规范连接分支中存在的各向同性流体的 Bianchi-I 宇宙学。 对于所考虑的两个连接分支，我们从$f(Q)$中的通用 Bianchi-I 宇宙学场方程出发，并提出了一种方法，一旦提供了$f(Q)$理论，就可以根据标准哈勃归一化的无量纲动力学变量构造一个自治动力系统。 特别注意区分了所考虑的每个模型在相空间中的物理可行区域。 结果发现，对于所考虑的两个连接分支，Kasner 解在所有考虑的模型中都会轻微违反有效引力耦合正性的关键物理可行性条件（$f_Q>0$），而除了共存规范连接中的单项式模型这一非常特殊的情况外，所有模型中都出现了物理可行的 de-Sitter 未来吸引子。 在早期宇宙宇宙学的背景下，我们发现，在共存规范下，均匀扰动的膨胀 FLRW 宇宙的各向同化是一个与模型无关的普遍特征，而在均匀扰动的预反弹 ekpyrotic 收缩 FLRW 宇宙中，各向同化虽然不完全普遍，但是一种可能的情景。 显示英文摘要

摘要： In this article, we present a generic dynamical system formulation for Bianchi-I cosmology in the presence of an isotropic fluid within the coincident gauge connection branch and one of the non-coincident gauge connection branches of $f(Q)$ gravity theory. For both the connection branches under consideration, we start from the generic Bianchi-I cosmological field equations in $f(Q)$ and present a prescription of how one can construct an autonomous dynamical system in terms of the standard Hubble-normalized dimensionless dynamical variables once an $f(Q)$ theory is provided. Particular care has been taken to single out the physically viable regions in the phase space for each of the models under consideration. This results in the finding that, for both of the connection branches under consideration, the Kasner solution marginally violates the key physical viability condition of positive effective gravitational coupling ($f_Q>0$) for all the models considered, whereas a physically viable de-Sitter future attractor appears in all the models, except for the very special case of the monomial model within the coincident gauge connection. In the context of the early universe cosmology, we find that isotropization of a homogeneously perturbed inflating FLRW universe is a generic model-independent feature in the coincident gauge, whereas the isotropization of a homogeneously perturbed pre-bounce ekpyrotically contracting FLRW universe is, although not completely generic, but a likely scenario.