We consider non-singular bouncing cosmologies , such as the new ekpyrotic model , in which the universe undergoes a slow contraction phase with equation of state w \gg 1 , followed by a bounce that occurs at a finite scale factor when quantum gravity corrections are still negligible .
Such a non-singular bounce requires a violation of the null energy condition in which w falls below -1 at some time before the bounce .
In this paper , we show that a component of the adiabatic curvature perturbations , though decaying and negligible during the ekpyrotic phase , is exponentially amplified just before w approaches -1 , enough to spoil the scale-invariant perturbation spectrum .
We discuss how the problem may be avoided , for example , in singular bounces .