The matching condition of Region I and II, Region IV and V are completely the same as in the flat plateau case, so here we only write down the matching condition between Region II and IV:

$$\begin{aligned}
v_2(0) = v_4 (0),\quad v'_2(0) = v'_4 (0) ,\end{aligned}$$

which can be written in terms of the more convenient matrix form $$\begin{aligned}
\begin{pmatrix}
\tau_B^{1-q_1} & \tau_B^{q_1} \\ (1-q_1) \tau_B^{-q_1} & q_1
\tau_B^{q_1-1} 
\end{pmatrix} \begin{pmatrix}
c_{21} \\ c_{22}
\end{pmatrix} = \begin{pmatrix} 
\tau_B^{1-q_1} & \tau_B^{q_1} \\ -(1-q_1) \tau_B^{-q_1} & -q_1
\tau_B^{q_1-1}
\end{pmatrix} \begin{pmatrix}
c_{41} \\ c_{42}
\end{pmatrix}.\end{aligned}$$ Combining these matching results we obtain the power spectrum completely the same as that of the instantaneous matching of the previous section.

Numerical Examples
------------------

In Fig. \[bounceplot1\] we show the form of the spectrum of cosmological perturbations and its tilt as a function of the comoving wavenumber $k$ for the two models we have considered in the previous sections.

We can clearly identify in Fig. \[bounceplot1\](a) the characteristic scales for each of the two models we have defined in Sec. \[sec2\]. For the flat plateau model (Model 1), there are two relevant comoving scales,

$$\begin{aligned}
&&k_{*,{\rm flat}}= \frac{q_1}{\tau_B-\Delta},
\label{kflat}
\\ &&k_{*,{\rm osc}}= \frac{q_1}{\tau_B}.
\label{kosc}\end{aligned}$$

In model 1 