Unstable growth of curvature perturbations in nonsingular bouncing cosmologies

Bouncing cosmologies require an ekpyrotic contracting phase (w1) in order to achieve flatness, homogeneity, and isotropy. Models with a nonsingular bounce further require a bouncing phase that violates the null energy condition (w<-1). We show that the transition from the ekpyrotic phase to the bouncing phase creates problems for cosmological perturbations. 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.