In addition to recent theoretical no-go theorems for a P(X) theory driving a cosmological bounce, there are also observational 'no-go's. The tensor-to-scalar ratio has been severely constrained by Planck, and in order for most P(X) theories to give a consistently small ratio the sound speed must be sufficiently small (this enhanced curvature perturbations). However, computing the non-Gaussianity from the primordial three-point correlation functions during matter-dominated contraction, one finds that such a small sound speed results in excessive non-Gaussianity.

Demanding that a P(X) driven bounce be consistent with observed tensor-to-scalar ratio and non-Gaussianity is incredibly restrictive. In the few cases where one is within experimental bounds, the non-Gaussianity is typically high enough to be measured by upcoming observations.