  In this article we want to answer the cosmologically relevant question what,
with some good semantic and physical reason, could be called the mass of an
infinitely extended, homogeneously matter-filled and expanding universe. To
answer this question we produce a space-like sum of instantaneous cosmic energy
depositions surrounding equally each spacepoint in the homogeneous universe. We
calculate the added-up instantaneous cosmic energy per volume around an
arbitrary space point in the expanding universe. To carry out this sum we use
as basic metrics an analogy to the inner Schwarzschild metric applied to stars,
but this time applied to the spacepoint-related universe. It is then shown that
this leads to the added-up proper energy within a sphere of a finite outer
critical radius defining the point-related infinity. As a surprise this radius
turns out to be reciprocal to the square root of the prevailing average cosmic
energy density. The equivalent mass of the universe can then also be calculated
and, by the expression which is obtained here, shows a scaling with this
critical radius of this universe, a virtue of the universe which was already
often called for in earlier works by E.Mach, H.Thirring and F.Hoyle and others.
This radius on the other hand can be shown to be nearly equal to the
Schwarzschild radius of the so-defined mass of the universe.
