Scalar field potentials for closed and open cosmological models

TL;DR

This paper presents a method to reconstruct scalar and tachyon field potentials that produce specific cosmological evolutions in closed and open isotropic models, providing explicit potentials for various matter contents.

Contribution

It introduces a novel technique for potential reconstruction in open and closed cosmologies, including scalar and tachyon fields, for different matter scenarios.

Findings

Reconstructed potentials for scalar fields with generic barotropic fluids and radiation plus cosmological constant.

Explicit potentials for tachyon and pseudo-tachyon fields in special cases.

Applicable to modeling different cosmological evolutions.

Abstract

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.