Can background cosmology hold the key for modified gravity tests?

TL;DR

This paper shows that background cosmology alone can rule out certain modified gravity theories, like $f(R)$ models, if their predicted expansion histories conflict with observations or local gravity tests.

Contribution

It demonstrates that background cosmology can be a powerful tool to constrain classes of modified gravity theories without resorting to complex nonlinear regime analyses.

Findings

Certain models cannot produce observed background expansion histories.

Deviations from $ ext{Lambda}$CDM can exclude specific $f(R)$ gravity models.

Background cosmology constraints are sufficient to test some modified gravity theories.

Abstract

Modified gravity theories are a popular alternative to dark energy as a possible explanation for the observed accelerating cosmic expansion, and their cosmological tests are currently an active research field. Studies in recent years have been increasingly focused on testing these theories in the nonlinear regime, which is computationally demanding. Here we show that, under certain circumstances, a whole class of theories can be ruled out by using background cosmology alone. This is possible because certain classes of models (i) are fundamentally incapable of producing specific background expansion histories, and (ii) said histories are incompatible with local gravity tests. As an example, we demonstrate that a popular class of models, $f(R)$ gravity, would not be viable if observations suggest even a slight deviation of the background expansion history from that of the $\Lambda$CDM paradigm.