  In this lecture I present the line elements that express the Hubble
expansion. The coordinates here are the spatial coordinates $x$, $y$, $z$, and
the velocity coordinate $v$, which are actually what astronomers use in their
measurements. Two such line elements are presented: the first is the empty
space (no matter exists), and the second with matter filling up the Universe.
These line elements are the comparable to the standard ones, the Minkowski and
the FRW line elements in ordinary general relativity theory.
