Matter instability in modified gravity

The Dolgov-Kawasaki instability discovered in the matter sector of the modified gravity scenario incorporating a -μ4/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+αμ2(n+1)/Rn, where α and n are real constants and n>0, are ruled out for any negative value of α