Consequences from conservation of the total density of the universe during the expansion

Abstract

The recent Cosmic Microwave Background (CMB) experiments have shown that the average density of the universe is close to the critical one and the universe is asymptotically flat (Euclidean). Taking into account that the universe remains flat and the total density of the universe $\Omega_{0}$ is conserved equal to a unit during the cosmological expansion, the Schwarzschild radius of the observable universe has been determined equal to the Hubble distance $R_{s}=2GM/c^{2}=R\sim c/H$, where M is the mass of the observable universe, R is the Hubble distance and H is the Hubble constant. Besides, it has been shown that the speed of the light c appears the parabolic velocity for the observable universe $c=\sqrt{2GM/R}=v_{p}$ and the recessional velocity $v_{r}=Hr$ of an arbitrary galaxy at a distance r > 100 Mps from the observer, is equal to the parabolic velocity for the sphere, having radius r and a centre, coinciding with the observer. The requirement for conservation of $\Omega_{0}=1$ during the expansion enables to derive the Hoyle-Carvalho formula for the mass of the observable universe $M=c^{3}/(2GH)$ by a new approach. Key words: flat universe; critical density of the universe; Schwarzschild radius; mass of the universe; parabolic velocity