标题： 标量场-物质相互作用模型在各向异性宇宙中的平均动力学：局部旋转对称的 Bianchi I 宇宙时空 显示英文标题

标题： Averaging Dynamics of Scalar Field-Matter Interacting Models in Anisotropic Universes: The Locally Rotationally Symmetric Bianchi I Spacetime

摘要： 我们考虑一个各向异性宇宙学模型，该模型基于局部旋转的Bianchi I时空，结合了标量场和非零的宇宙相互作用项。采用平均值理论框架来研究相关的非线性微分方程。通过对引力场方程进行定性分析，我们获得了关于各向异性标量场模型在广义谐波势下的解空间结构的重要见解。标量场与物质之间的相互作用由一个依赖于哈勃参数、标量场的时间导数以及冷暗物质和暗能量的能量密度的一般表达式来描述。这种表述涉及调节相互作用的真实参数，以及一个具有哈勃参数维度的耦合常数。我们证明哈勃参数作为时间依赖的扰动参数，控制全系统与其时间平均对应物之间的差异。随着该参数的减小，两个系统都趋于相同的渐近行为。这使得振荡效应得以抑制，显著简化了动力学分析。最后，我们确定了相互作用参数的条件，以确保系统的演化是正则的，从而防止奇点的出现。 显示英文摘要

摘要： We consider an anisotropic cosmological model based on the locally rotational Bianchi I spacetime, incorporating a scalar field and a non-zero cosmological interaction term. The framework of averaging theory is employed to study the associated non-linear differential equations. Through a qualitative analysis of the gravitational field equations, we obtain valuable insights into the structure of the solution space for the anisotropic scalar field model with a generalized harmonic potential. The interaction between the scalar field and matter is described by a general expression that depends on the Hubble parameter, the time derivative of the scalar field, and the energy densities of cold dark matter and dark energy. This formulation involves real parameters that modulate the interaction, as well as a coupling constant with the dimensions of the Hubble parameter. We show that the Hubble parameter serves as a time-dependent perturbation parameter, controlling the discrepancy between the full system and its time-averaged counterpart. As this parameter decreases, both systems converge to the same asymptotic behaviour. This enables the suppression of oscillatory effects, significantly simplifying the dynamical analysis. Finally, we identify conditions on the interaction parameters that ensure the regularity of the system's evolution by preventing the emergence of singularities.