Under the premise that the current observations of the cosmic background radiation set a very stringent limit to the anisotropy of the universe, we present a proposal where the dark side of the universe is represented by one parameter, $\rm m_\phi$, with the aim of having a time-varying cosmological term $\Lambda(t)$ in the dust epoch within an anisotropic cosmology and from there obtaining a scalar field potential that gives the inflationary behavior and isotropy to this day, we introduce the fluctuation deceleration parameter $\rm \Delta q(t)$ obtaining a negative value, where we consider two epoch in our universe, stiff and dust scenarios, which indicate that the universe has growing expansion in its overage function volume. The main idea arises by the hypothesis that the cosmological term $\Lambda$ is identified with the scalar potential as $\rm V(\phi(t))=2\Lambda(t)$. As a consequence of scaling solutions between the energy density of the scalar field and ordinary matter, exact solutions of the field equations are obtained by a special ansatz to solve the Einstein-Klein-Gordon (EKG) equation and the particular potential obtained by this approach. We use Misner's variables considering a decomposition in an isotropic and an anisotropic part. We employ the Lagrangian formalism for a scalar field $\phi$ with standard kinetic energy and arbitrary scalar potential $\rm V(\phi)$.

中文翻译：

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尘埃时代的宇宙学体积加速：在各向异性宇宙学模型中使用标度解和可变宇宙学术语 $\Lambda (t)$

主要思想源于宇宙学术语 $\Lambda$ 与标量势相同的假设，即 $\rm V(\phi(t))=2\Lambda(t)$。由于标量场的能量密度与普通物质之间的比例解的结果，场方程的精确解是通过一个特殊的 ansatz 来求解爱因斯坦-克莱因-戈登 (EKG) 方程和通过这种方法获得的特定势能. 我们使用 Misner 变量来考虑各向同性和各向异性部分的分解。我们对具有标准动能和任意标量势 $\rm V(\phi)$ 的标量场 $\phi$ 使用拉格朗日形式主义。场方程的精确解是通过一个特殊的 ansatz 来求解爱因斯坦-克莱因-戈登 (EKG) 方程和通过这种方法获得的特定势得到的。我们使用 Misner 变量来考虑各向同性和各向异性部分的分解。我们对具有标准动能和任意标量势 $\rm V(\phi)$ 的标量场 $\phi$ 使用拉格朗日形式主义。场方程的精确解是通过一个特殊的 ansatz 来求解爱因斯坦-克莱因-戈登 (EKG) 方程和通过这种方法获得的特定势得到的。我们使用 Misner 变量来考虑各向同性和各向异性部分的分解。我们对具有标准动能和任意标量势 $\rm V(\phi)$ 的标量场 $\phi$ 使用拉格朗日形式主义。