Inverse problem - reconstruction of dark energy models

TL;DR

This paper reviews methods to reconstruct various modified gravity models that can replicate any observed universe development, providing explicit formulas especially using e-foldings related to redshift.

Contribution

It presents explicit reconstruction formulas for multiple gravity models based on observed universe expansion, facilitating model building from future observational data.

Findings

Formulas for reconstructing gravity models from Hubble rate data

Use of e-foldings to relate models to redshift observations

Demonstrates the variety of models compatible with observed universe expansion

Abstract

We review how we can construct the gravity models which reproduces the arbitrary development of the universe. We consider the reconstruction in the Einstein gravity coupled with generalized perfect fluid, scalar-Einstein gravity, scalar-Einstein-Gauss-Bonnet gravity, Einstein-$F(G)$-gravity, and $F(R)$-gravity. Very explicit formulas are given to reconstruct the models, which could be used when we find the detailed data of the development of the universe by future observations. Especially we find the formulas using e-foldings, which has a direct relation with observed redshift. As long as we observe the time development of the Hubble rate $H$, there exists a variety of models describing the arbitrary development of universe.