Imprints of intrinsic and exterior curvatures in cosmology

Nowadays, according to the observational evidences the curvature parameter of the universe is neglected and spatially flat FLRW model is on the top of interest for cosmologists. However, due to some discrepancies between $\Lambda$-CDM model anticipations and observations, one may think out the curvature parameter as the solution even though it may be very small. So, in this article we investigate the eras in which the curvature influence was or is more significant. In addition, a geometrical interpretation of Hubble parameter is dedicated. We find that the Hubble parameter is more appropriate to be defined as the mean curvature of the spatial section of the universe because the concept of the scale factor in a non-homogeneous universe is not precisely clear.
Comment: 11 pages, version published in Gravit. Cosmol