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Modified gravity theories are a popular alternative to dark energy as apossible explanation for the observed accelerating cosmic expansion, and theircosmological tests are currently an active research field. Studies in recentyears have been increasingly focused on testing these theories in the nonlinearregime, which is computationally demanding. Here we show that, under certaincircumstances, a whole class of theories can be ruled out by using backgroundcosmology alone. This is possible because certain classes of models (i) arefundamentally incapable of producing specific background expansion histories,and (ii) said histories are incompatible with local gravity tests. As anexample, we demonstrate that a popular class of models, $f(R)$ gravity, wouldnot be viable if observations suggest even a slight deviation of the backgroundexpansion history from that of the $\Lambda$CDM paradigm.

Can background cosmology hold the key for modified gravity tests?