Imprints of intrinsic and exterior curvatures in cosmology

TL;DR

This paper explores the role of intrinsic and extrinsic curvature in cosmology, examining when curvature effects are significant and proposing a geometric interpretation of the Hubble parameter as the mean curvature of the universe's spatial section.

Contribution

It investigates the significance of curvature throughout cosmic history and offers a novel geometric interpretation of the Hubble parameter as the mean curvature of spatial sections.

Findings

Curvature effects were more significant in earlier cosmic eras.

The Hubble parameter can be interpreted as the mean curvature of spatial slices.

This interpretation clarifies the concept of the scale factor in non-homogeneous universes.

Abstract

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.