Scalar field evolution at background and perturbation levels for a broad class of potentials

TL;DR

This paper develops a unified dynamical system approach to study scalar field evolution and perturbations in cosmology for a broad class of potentials, using the $f$-deviser method, with applications to monomial and double exponential potentials.

Contribution

It introduces the $f$-deviser method for a unified analysis of scalar field background and perturbations with arbitrary potentials.

Findings

Unified dynamical system framework for background and perturbations.

Analysis of linear perturbations for monomial and double exponential potentials.

Evolution of Bardeen potentials with matter included.

Abstract

In this paper, we investigate a non-interacting scalar field cosmology with an arbitrary potential using the $f$-deviser method that relies on the differentiability properties of the potential. Using this alternative mathematical approach, we present a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary potentials. For illustration, we consider a monomial and double exponential potential. These two classes of potentials comprise the asymptotic behaviour of several classes of scalar field potentials, and, therefore, they provide the skeleton for the typical behaviour of arbitrary potentials. Moreover, we analyse 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. Finally, an exhaustive dynamical system analysis for each scalar perturbation is presented, including the evolution of Bardeen potentials in the presence of matter.