Cosmological Theories of Special and General Relativity - II

Abstract

Astronomers measure distances to faraway galaxies and their velocities. They do that in order to determine the expansion rate of the Universe. In Part I of these lectures the foundations of the theory of the expansion of the Universe was given. In this part we present the theory. A formula for the distance of the galaxy in terms of its velocity is given. It is very simple: $r(v)=cτ/β\sinhβv/c$, where $τ$ is the Big Bang time, $β=\sqrt{1-Ω_m}$, and $Ω_m$ is the mass density of the Universe. For $Ω_m<1$ this formula clearly indicates that the Universe is expanding with acceleration, as experiments clearly show.