cosmological scale factor. It will be convenient to use conformal time $\tau$ related to the physical time via $dt = a(t) d\tau$. We will consider only linear cosmological perturbations (see, e.g., Ref. [@MFB] for a comprehensive review). In this case, fluctuations evolve independently in Fourier space. We will label the fluctuation modes in terms of their comoving wave number $k$.

We consider a non-singular symmetric bouncing cosmology in which the cosmological scale factor $a(\tau)$ has the form shown in Fig. \[bounceplot\], i.e., for which $a(\tau)$ has one “oscillation” between the onset and end of the bounce phase. We consider the two forms depicted in Fig. \[bounceplot\], with one peak between the time $- \tau_B$ when $a(\tau)$ reaches its first minimum, and the time $+ \tau_B$ when the second minimum of $a(\tau)$ is taken on. Specifically, we consider two specific models: Model 1, with a flat plateau about $\tau = 0$; and the Model 2, with a kink of $a(\tau)$ at $\tau = 0$, which is the limiting case of the first model when the duration of the flat plateau equals to zero. The time interval of the plateau region is $-\Delta < \tau < \Delta$ given by some conformal time 