Dark energy, antimatter gravity and geometry of the Universe
  This article is based on two hypotheses. The first one is the existence of
the gravitational repulsion between particles and antiparticles. Consequently,
virtual particle-antiparticle pairs in the quantum vacuum may be considered as
gravitational dipoles. The second hypothesis is that the Universe has geometry
of a four-dimensional hyper-spherical shell with thickness equal to the Compton
wavelength of a pion, which is a simple generalization of the usual geometry of
a 3-hypersphere. It is striking that these two hypotheses lead to a simple
relation for the gravitational mass density of the vacuum, which is in very
good agreement with the observed dark energy density.
