Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?

TL;DR

This paper investigates whether certain $F(R)$ modified gravity models can replicate General Relativity with a cosmological constant throughout cosmic history, finding they require fine-tuning and mimic standard gravity with suppressed corrections.

Contribution

The study demonstrates that consistent $F(R)$ models satisfying known constraints effectively mimic GR+$\Lambda$ with suppressed deviations, highlighting the necessity of fine-tuning.

Findings

Models must mimic GR+$\Lambda$ with suppressed corrections

Fine-tuning of parameters is required for late-time acceleration

Constraints restrict $F(R)$ functions to resemble standard gravity

Abstract

Modified gravity models are subject to a number of consistency requirements which restrict the form that the function $F(R)$ can take. We study a particular class of $F(R)$ functions which satisfy various constraints that have been found in the literature. These models have a late time accelerating epoch, and an acceptable matter era. We calculate the Friedmann equation for our models, and show that in order to satisfy the constraints we impose, they must mimic General Relativity plus $\Lambda$ throughout the cosmic history, with exponentially suppressed corrections. We also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase. We discuss the generality of this conclusion.