Reconstruction of Scalar Potentials in Modified Gravity Models

TL;DR

This paper introduces a superpotential method for reconstructing scalar field potentials in modified gravity models, enabling the derivation of cosmological solutions without predefining the Hubble parameter, and applies it to de Sitter and other cosmologies.

Contribution

It presents a novel superpotential technique for reconstructing scalar potentials in non-minimally coupled gravity models, expanding the toolkit for cosmological model building.

Findings

Reconstructed scalar potentials for de Sitter solutions.

Derived potentials matching Einstein-Hilbert plus perfect fluid evolution.

Provided a method to determine scalar field dynamics without fixing the Hubble parameter.

Abstract

We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained.