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

Curvature and topology dependency of the cosmological spectra