Abstract
First, I will discuss which theories can allow for a "healthy" bounce: a smooth evolution of a spatially flat Friedmann universe from contraction to expansion without ghosts and gradient instabilities. Further, I will talk about cosmological time crystals recently introduced by Wilczek. The latter are systems with limit cycles and can represent vacuum with minimally broken time-translation invariance. In particular, these systems can model Dark Energy with rapidly oscillating equation of state. I will argue that all such theories not only violate the Null Energy Condition, but also necessarily possess states with superluminality. Even though the bouncing solution can be completely subluminal. This superluminality has crucial consequences for a potential completion.