Matter instability in modified gravity

The Dolgov-Kawasaki instability discovered in the matter sector of the modified gravity scenario incorporating a $-{\mu }^4/R$ correction to Einstein gravity is studied in general $f(R)$ theories. A stability condition is found in the metric version of these theories to help ruling out models that are unviable from the theoretical point of view. For example, the theories $f(R)=R+\alpha {\mu }^{2(n+1)}/R^n$, where $\alpha$ and $n$ are real constants and $n>0$, are ruled out for any negative value of $\alpha$.