Generic Instabilities of Non-Singular Cosmologies

Abstract

The null energy condition can be violated stably in general scalar-tensor theories of gravity, which gives rise to the possibilities of healthy non-singular cosmologies. However, it has been reported that in many cases cosmological solutions are plagued with instabilities or have some pathologies somewhere in the whole history of the universe. We show that non-singular models (with flat spatial sections) in general suffer either from gradient instabilities or some kind of pathology in the tensor sector. This implies that one must go beyond the Horndeski theory to implement healthy non-singular cosmologies.