  One can make the very simple hypothesis that the Universe is the inside of an
hypersphere in 4 dimensions, where our 3-dimensional world consists of
hypersurfaces at different radii. Based on this assumption it is possible to
show that Universe expansion at a rate corresponding to flat comes as a direct
geometrical consequence without intervening critical density; any mass density
is responsible for opening the Universe and introduces a cosmological constant.
Another consequence is the appearance of inertia swirls of expanding matter,
which can explain observed velocities around galaxies, again without the
intervention of dark matter. When restricted to more everyday situations the
model degenerates in what has been called 4-dimensional optics; in the paper
this is shown to be equivalent to general relativity in all static isotropic
metric situations. In the conclusion some considerations bring the discussion
to the realm of 4D wave optics.
