Generic instabilities of non-singular cosmologies in Horndeski theory: a no-go theorem

TL;DR

This paper proves a no-go theorem showing that non-singular cosmologies within the full Horndeski theory inevitably face instabilities or pathologies, indicating the need to explore theories beyond Horndeski for healthy models.

Contribution

It extends the no-go theorem to the full Horndeski theory, demonstrating the generic presence of instabilities in non-singular cosmologies within this framework.

Findings

Non-singular models in Horndeski theory suffer from instabilities.

Gradient and tensor sector pathologies are unavoidable in these models.

Healthy non-singular cosmologies require theories beyond Horndeski.

Abstract

The null energy condition can be violated stably in generalized Galileon theories, 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. Recently, this was shown to be generically true in a certain subclass of the Horndeski theory. In this short paper, we extend this no-go argument to the full Horndeski theory, and 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.