of interest, and hence we cannot just focus on the dominant modes because for those small time durations the subdominant modes can also have an effect on the primordial power spectra. We need to keep all the contributions and give a comprehensive analysis.

This paper is organized as follows. In Sec. \[sec2\], we specify our setup for the intermediate small bounce feature and discuss about the relevant scales involved. In Sec. \[sec3\], we present the calculation of power spectrum. A detailed presentation of the required matching conditions is given and the specific results are given for the two specific small inter bounce features we considered. An analysis of these results for the power spectrum is then given in Sec. \[sec4\]. In Sec. \[sec5\], we give a generalization for the case of a large number of small bounces. In Sec. \[sec6\] we present our conclusions. An appendix is included to discuss some of the technical details.

Setup {#sec2}
=====

We will consider a spatially flat Friedmann-Lemaitre-Robertson-Walker space-time in which the metric is given by $$ds^2 \, = \, dt^2 - a(t)^2 d{\bf x}^2 \, ,$$ where $t$ is physical time, ${\bf x}$ are the comoving spatial coordinates, and $a(t)$ is the 