Superpotential method for $F(R)$ cosmological models

TL;DR

This paper develops a method using superpotentials and conformal transformations to find exact $F(R)$ gravity models, providing explicit functions and detailed solutions for specific models like $R^2$ gravity with a cosmological constant.

Contribution

It introduces a novel approach combining superpotential techniques and conformal transformations to derive explicit $F(R)$ functions with exact solutions.

Findings

Explicit $F(R)$ functions constructed for specific models.

Exact solutions obtained for $R^2$ gravity with cosmological constant.

Method demonstrated to produce models with known analytical solutions.

Abstract

We construct the $F(R)$ gravity models with exact particular solutions using the conformal transformation and the superpotential method for the corresponding models in the Einstein frame. The functions $F(R)$ are obtained explicitly. We consider exact solutions for the obtained $R^2$ gravity model with the cosmological constant in detail.