Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch

TL;DR

This paper examines modified $f(R)$ gravity models with an effective cosmological constant, highlighting their potential to pass solar system and cosmological tests but also revealing issues like Newton law corrections and matter instability.

Contribution

It identifies the limitations of certain $f(R)$ models, particularly regarding Newton law corrections and matter instability, suggesting the need for more complex theories.

Findings

Some $f(R)$ models exhibit significant Newton law corrections in the future universe.

Models with acceptable Newton law behavior suffer from matter instability.

More complex or extended models are needed to resolve these issues.

Abstract

We consider class of modified $f(R)$ gravities with the effective cosmological constant epoch at the early and late universe. Such models pass most of solar system tests as well they satisfy to cosmological bounds. Despite their very attractive properties, it is shown that one realistic class of such models may lead to significant Newton law corrections which become small at the future universe only. The model with acceptable Newton law regime shows the matter instability. This suggests that more complicated version of such theory (or extended parameters space) should be investigated.