In this paper, a non-interacting scalar field cosmology with an arbitrary potential using the f-deviser method that relies on the differentiability properties of the potential is investigated. Using this alternative mathematical approach, a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary potentials is presented. For illustration, a monomial and double exponential potential is considered. These two classes of potentials comprise the asymptotic behavior of several classes of scalar field potentials, and, therefore, they provide the skeleton for the typical behavior of arbitrary potentials. Moreover, the linear cosmological perturbations in the matterless case by considering three scalar perturbations: the evolution of the Bardeen potentials, the comoving curvature perturbation, the so-called Sasaki-Mukhanov variable, or the scalar field perturbation in uniform curvature gauge is analyzed. Finally, an exhaustive dynamical system analysis for each scalar perturbation is presented, including the evolution of Bardeen potentials in the presence of matter.

中文翻译：

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各种势的背景和扰动水平下的标量场演化

在本文中，使用依赖于势的可微性性质的f -deviser 方法研究了具有任意势的非相互作用标量场宇宙学。使用这种替代数学方法，提出了标量场背景和具有任意势的扰动水平的统一动力系统分析。为了便于说明，考虑单项式和双指数势。这两类势包含几类标量场势的渐近行为，因此，它们为任意势的典型行为提供了骨架。此外，通过考虑三种标量扰动：巴丁势的演化、同动曲率扰动、所谓的Sasaki-Mukhanov变量或均匀曲率规范中的标量场扰动，分析了无物质情况下的线性宇宙扰动。最后，对每个标量扰动进行了详尽的动力系统分析，包括物质存在下巴丁势的演化。