Curvature of the universe and the dark energy potential

Abstract

The flatness of an accelerating universe model (characterized by a dark energy scalar field $χ$) is mimicked from a curved model that is filled with, apart from the cold dark matter component, a quintessencelike scalar field $Q$. In this process, we characterize the original scalar potential $V(Q)$ and the mimicked scalar potential $V(χ)$ associated to the scalar fields $Q$ and $χ$, respectively. The parameters of the original model are fixed through the mimicked quantities that we relate to the present astronomical data, such that the equation state parameter $w_{_χ}$ and the dark energy density parameter $Ω_χ$.