this is not satisfied then we recover the results for the second model, given by the plots on the right shown in Fig. \[bounceplot\]). Modes with wavelength smaller than $k_*^{-1}$ enter the Hubble radius during Phase II and exit again during Phase IV. Modes with $k_*^{-1} < k^{-1}
< k_{\Delta}^{-1}$ are inside the Hubble radius only during Phase III. For these modes the matching occurs at times $- \Delta$ and $+
\Delta$. This is also true for modes with $k^{-1} > k_{\Delta}^{-1}$. These modes, however, undergo a negligible amount of oscillations in Phase III. In the case that $k_\Delta^{-1}>k_*^{-1}$, we have three different behaviors of the power spectrum. For the very large scale modes $k^{-1}\gg k_\Delta^{-1}$, the power spectrum does not feel the influence of the small bump of the scale factor. For the modes $k_*^{-1}<k^{-1}<k_\Delta^{-1}$, there is a complicated change of the power spectrum induced by the flat plateau. For the modes $k^{-1}<k_*^{-1}$, the change of the power spectrum approaches the well known result for cyclic cosmologies [@RHBcyclic], as we will explicitly verify later on below. In the case that $k_\Delta^{-1}<k_*^{-1}$, there is only one characteristic scale $k_*^{-1}$. The mode with $k^{-1}>k_*^{-1}$ will not feel the influence of the 