.\end{aligned}$$

The first conclusion we draw from this result is that the shape of the spectrum for large scale modes does not change during the bounce. This agrees with the conclusions of previous work on simple bounce models [@matterBounce-2]. The amplitude, on the other hand, is amplified. Recall that $2q_i - 1 > 0$, and that $\epsilon \ll \tau_B$. Hence, it is the second term in Eq. (\[powerspectrum1\]) which dominates, and we conclude that the amplitude of the spectrum is amplified by a factor of $${\cal A} \, = \, A_2^2 \bigg(\frac{\tau_B}{\epsilon}\bigg)^{4q_1 - 2} .
\label{Amplitude}$$ This result can also be understood easily: Fluctuations grow both in the contracting and in the expanding phase. In fact, the fluctuations diverge in the limit when the scale factor becomes zero. Hence, without an effective cutoff $\epsilon$ we would get a divergence in the spectrum. With a cutoff, the enhancement factor of the amplitude of the power spectrum will be determined by the dimensionless ratio between $\tau_B$ and $\epsilon$ to a power which depends on the growth rate of the fluctuations on super-Hubble scales, i.e., on $q_1$ (see the discussion of these issues in a more general context in the review article Ref. 