  In this article we investigate dependency of the adiabatic and entropy
spectral indices of the cosmological perturbations on the geometry and topology
of the background universe. Our discussion includes the post-inflationary
universe i.e. radiation-dust mixture era. For this purpose, we first extract an
explicit equation describing evolution of the comoving curvature perturbation
in the FLRW universe with arbitrary spatial sectional curvature. We may percept
when $K\neq 0$, curvature scale would be as significant as the perturbations
scales to recognize the behavior of the spectral indices. We also focus on the
entropy perturbation in order to extract behavior of the isocurvature spectral
index in terms of the curvature index and time. Our analysis shows that spectra
of curvature and entropy perturbations in sub-horizon scales could be function
of topology. Moreover, an accurate analysis makes clear that time-average of
isocurvature index in case $K=0$ is about zero,so that imprint of entropy
perturbation in time duration may be negligible. We also consider evolution of
the cosmological indices for super-curvature modes in the case $K=-1$. In the
most results dependency to curvature, initial conditions and scale modes are
thoroughly vivid.
