Curvature of the universe and the dark energy potential

TL;DR

This paper explores how a curved universe model with a scalar field can be mimicked by a flat universe with a different scalar field, relating their potentials and parameters to current astronomical data.

Contribution

It introduces a method to replicate a curved universe with dark energy scalar fields using a flat universe model, linking their potentials and observational parameters.

Findings

Scalar potentials V(Q) and V(χ) are characterized and related.

The model parameters are fixed using current astronomical data.

The approach connects curvature effects with dark energy properties.

Abstract

The flatness of an accelerating universe model (characterized by a dark energy scalar field $\chi$) 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 $V(\chi)$ associated to the scalar fields $Q$ and $\chi$, 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 $w_{_{\chi}}$ and the dark energy density parameter $\Omega_{\chi}$.