The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes With Time

TL;DR

This paper rigorously demonstrates that the spatial curvature in the Robertson-Walker metric is not constant when the scale factor R(t) varies with time, challenging traditional assumptions and implications in cosmology.

Contribution

It provides a strict Riemannian geometric calculation showing the curvature parameter k does not represent constant spatial curvature when R(t) changes, prompting a re-evaluation of cosmological models.

Findings

Spatial curvature is not constant when R(t) varies with time

The parameter k is not a fixed spatial curvature factor

Current cosmological estimates need re-assessment

Abstract

The real physics meaning of constant k in the Robertson-Walker metric is discussed when scalar factor R(t) is relative to time. Based on the curvature formula of the Riemannian geometry strictly, the spatial curvature of the R-W metric is calculated. The result indicates that the spatial curvature of the R-W metric is not a constant when R(t) changes with time and the constant in the R-W metric k does not represent spatial curvature factor. It can only be considered as an adjustable parameter relative to the Hubble constant. The result is completely different from the current understanding which is based on specious estimation actually, in stead of strict calculation. In light of this result, many conclusions in the current cosmology, such as the values of the Hubble constant, dark material and dark energy densities, should be re-estimated. In this way, we may get rid of the current puzzle situation of cosmology thoroughly.