Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann–Lemaître–Robertson–Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered. Asymptotic methods and averaging theory are used to obtain relevant information about the solution space. In this approach, the Hubble parameter plays the role of a time-dependent perturbation parameter which controls the magnitude of the error between full-system and time-averaged solutions as it decreases. Our approach is used to show that full and time-averaged systems have the same asymptotic behavior. Numerical simulations are presented as evidence of such behavior. Relevant results show that the asymptotic behavior of the solutions is independent of the coupling function.

中文翻译：

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相互作用标量场宇宙学的微扰分析

在平坦和负弯曲的 Friedmann-Lemaitre-Robertson-Walker 和 Bianchi I 度量中研究了具有广义谐波势的标量场宇宙学。考虑标量场和物质之间的相互作用。渐近方法和平均理论用于获取有关解空间的相关信息。在这种方法中，哈勃参数扮演着随时间变化的扰动参数的角色，它控制全系统解和时间平均解之间误差的大小，因为它会减小。我们的方法用于表明完整系统和时间平均系统具有相同的渐近行为。数值模拟作为这种行为的证据。相关结果表明解的渐近行为与耦合函数无关。