How to Measure the Cosmic Curvature

Abstract

The conventional method to determine the cosmic curvature is to measure the total mass density ${\Omega }_{\mathrm{tot}}$. Unfortunately the observational ${\Omega }_{\mathrm{tot}}$ is closely near the critical value 1. The computation of this paper shows that ${\Omega }_{\mathrm{tot}}\approx 1$ is an inevitable result for the young universe independent of the spatial topology. So the mass density is not a good criterion to determine the cosmic curvature. In this paper, we derive a new criterion based on the galactic distribution with respect to redshift $z$, which only depends on the cosmological principle and geometry. The different type of spatial topology will give different results, then the case can be definitely determined.

10 pages, 2 figures

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