Modified gravity and its reconstruction from the universe expansion history

TL;DR

This paper develops a reconstruction method for various modified gravity theories using the universe's expansion history, demonstrating their ability to produce realistic cosmological evolution including dark energy and acceleration phases.

Contribution

It introduces a unified reconstruction scheme for multiple modified gravity models based on observed universe expansion, including scalar-tensor, $f(R)$, $F(G)$, and scalar-Gauss-Bonnet theories.

Findings

Reconstructed models can reproduce matter dominance and acceleration epochs.

Late-time universe solutions can match $ ext{Lambda}$CDM with WMAP data.

Modified gravity models can incorporate dark energy without additional components.

Abstract

We develop the reconstruction program for the number of modified gravities: scalar-tensor theory, $f(R)$, $F(G)$ and string-inspired, scalar-Gauss-Bonnet gravity. The known (classical) universe expansion history is used for the explicit and successful reconstruction of some versions (of special form or with specific potentials) from all above modified gravities. It is demonstrated that cosmological sequence of matter dominance, decceleration-acceleration transition and acceleration era may always emerge as cosmological solutions of such theory. Moreover, the late-time dark energy FRW universe may have the approximate or exact $\Lambda$CDM form consistent with three years WMAP data. The principal possibility to extend this reconstruction scheme to include the radiation dominated era and inflation is briefly mentioned. Finally, it is indicated how even modified gravity which does not describe the matter-dominated epoch may have such a solution before acceleration era at the price of the introduction of compensating dark energy.