Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials

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