$\Delta$ with $\Delta < \tau_B$. The forms shown in Fig. \[bounceplot\] are simpler enough such as to allow an analytical study, but already of sufficient complexity such as to provide the main relevant features in the power spectrum that we might also observe in some more complex setup for the inter-bounce features. In particular, our results can be easily generalized to the case of many oscillations, as we will later discuss in Sec. \[sec5\].

As seen in Fig. \[bounceplot\], for the two forms shown the time interval can be divided into five intervals. The first is the initial contracting phase (Phase I) $\tau < - \tau_B$. The second is the intermediate expanding phase (Phase II). The third is Phase III with static scale factor, the fourth (Phase IV) is the intermediate contracting phase and Phase V is the final expanding phase. Fluctuation modes exit the Hubble radius in the initial contracting phase. The top panels in Fig. \[bounceplot\] give a sketch of the scale factor, the lower panels show the corresponding time evolution of the comoving Hubble radius. The vertical axis of the lower panels can also be viewed as a label for comoving wavelength. In this way, it is 